121:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial, métrico y variacional:@0.541231:0.043660:0.930030:0.043660:0.930030:0.024915:0.541231:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En toda elipse, :@0.744288:0.182661:0.843272:0.182661:0.843272:0.168376:0.744288:0.168376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
consideramos que::@0.744288:0.197789:0.869541:0.197789:0.869541:0.183505:0.744288:0.183505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.803078:0.305237:0.812933:0.305237:0.812933:0.296422:0.803078:0.296422:0.000000
b:@0.812932:0.305594:0.819463:0.305594:0.819463:0.295495:0.812932:0.295495:0.000000
b:@0.814411:0.228126:0.820942:0.228126:0.820942:0.218027:0.814411:0.218027:0.000000
a:@0.893572:0.273407:0.898944:0.273407:0.898944:0.263308:0.893572:0.263308:0.000000
2:@0.737001:0.273050:0.746856:0.273050:0.746856:0.264235:0.737001:0.264235:0.000000
a:@0.746856:0.273407:0.752227:0.273407:0.752227:0.263308:0.746856:0.263308:0.000000
y:@0.809343:0.215117:0.815524:0.215117:0.815524:0.203124:0.809343:0.203124:0.000000
x:@0.905805:0.276213:0.911832:0.276213:0.911832:0.264220:0.905805:0.264220:0.000000
x:@0.859956:0.234457:0.866155:0.234457:0.866155:0.221622:0.859956:0.221622:0.000000
:@0.861946:0.234906:0.867043:0.234906:0.867043:0.222290:0.861946:0.222290:0.000000
F:@0.761629:0.275985:0.767446:0.275985:0.767446:0.264824:0.761629:0.264824:0.000000
:@0.764052:0.274371:0.768484:0.274371:0.768484:0.263400:0.764052:0.263400:0.000000
1:@0.767419:0.278278:0.771206:0.278278:0.771206:0.271654:0.767419:0.271654:0.000000
   (:@0.771206:0.275985:0.791011:0.275985:0.791011:0.264624:0.771206:0.264624:0.000000:0.000000:0.000000:0.000000
5 2:@0.773802:0.275584:0.802098:0.275584:0.802098:0.265667:0.773802:0.265667:0.000000:0.000000:0.000000
c:@0.802098:0.275985:0.807635:0.275985:0.807635:0.264824:0.802098:0.264824:0.000000
, 0):@0.807635:0.275985:0.822569:0.275985:0.822569:0.264624:0.807635:0.264624:0.000000:0.000000:0.000000:0.000000
F:@0.836264:0.275985:0.842081:0.275985:0.842081:0.264824:0.836264:0.264824:0.000000
:@0.838687:0.274371:0.843119:0.274371:0.843119:0.263400:0.838687:0.263400:0.000000
2:@0.842052:0.278278:0.845839:0.278278:0.845839:0.271654:0.842052:0.271654:0.000000
   ( , 0):@0.845839:0.275985:0.887073:0.275985:0.887073:0.264624:0.845839:0.264624:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.848754:0.275584:0.859841:0.275584:0.859841:0.265667:0.848754:0.265667:0.000000
c:@0.866283:0.275985:0.871820:0.275985:0.871820:0.264824:0.866283:0.264824:0.000000
Figura 2.33.:@0.857831:0.327566:0.918019:0.327566:0.918019:0.316138:0.857831:0.316138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.744288:0.345374:0.752521:0.345374:0.752521:0.331341:0.744288:0.331341:0.000000
:@0.746932:0.343558:0.752504:0.343558:0.752504:0.329766:0.746932:0.329766:0.000000
   (x,  ) es un punto de :@0.751082:0.345374:0.908993:0.345374:0.908993:0.331089:0.751082:0.331089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.754680:0.344869:0.768619:0.344869:0.768619:0.332400:0.754680:0.332400:0.000000
y:@0.790022:0.345374:0.796816:0.345374:0.796816:0.331341:0.790022:0.331341:0.000000
la elipse.:@0.744288:0.360502:0.799988:0.360502:0.799988:0.346218:0.744288:0.346218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.744288:0.375631:0.751601:0.375631:0.751601:0.361599:0.744288:0.361599:0.000000
:@0.746848:0.373816:0.752421:0.373816:0.752421:0.360023:0.746848:0.360023:0.000000
1:@0.751005:0.378515:0.755766:0.378515:0.755766:0.370188:0.751005:0.370188:0.000000
 y   son los focos de la :@0.755722:0.375631:0.909152:0.375631:0.909152:0.361347:0.755722:0.361347:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.770197:0.375631:0.777510:0.375631:0.777510:0.361599:0.770197:0.361599:0.000000
:@0.772757:0.373816:0.778330:0.373816:0.778330:0.360023:0.772757:0.360023:0.000000
2:@0.776912:0.378515:0.781673:0.378515:0.781673:0.370188:0.776912:0.370188:0.000000
elipse.:@0.744280:0.390760:0.785371:0.390760:0.785371:0.376476:0.744280:0.376476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0 es el centro de la elipse.:@0.744280:0.405889:0.911003:0.405889:0.911003:0.391605:0.744280:0.391605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.746104:0.404074:0.751676:0.404074:0.751676:0.390281:0.746104:0.390281:0.000000
La suma de las distancias :@0.744280:0.421018:0.912504:0.421018:0.912504:0.406734:0.744280:0.406734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desde un punto   a los :@0.744280:0.436147:0.897510:0.436147:0.897510:0.421863:0.744280:0.421863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.853769:0.436147:0.862002:0.436147:0.862002:0.422115:0.853769:0.422115:0.000000
:@0.856413:0.434332:0.861986:0.434332:0.861986:0.420539:0.856413:0.420539:0.000000
puntos fijos llamados :@0.744263:0.451276:0.888067:0.451276:0.888067:0.436992:0.744263:0.436992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
focos es siempre :@0.744263:0.466405:0.857906:0.466405:0.857906:0.452121:0.744263:0.452121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
constante e igual a 2  con :@0.744263:0.481534:0.921073:0.481534:0.921073:0.467250:0.744263:0.467250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.880293:0.481534:0.888710:0.481534:0.888710:0.467502:0.880293:0.467502:0.000000
a:@0.744263:0.496663:0.752680:0.496663:0.752680:0.482631:0.744263:0.482631:0.000000
 > 0.:@0.752613:0.496663:0.780726:0.496663:0.780726:0.482379:0.752613:0.482379:0.000000:0.000000:0.000000:0.000000:0.000000
La ecuación cartesiana de :@0.744263:0.511792:0.918031:0.511792:0.918031:0.497508:0.744263:0.497508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la elipse con centro en el :@0.744263:0.526921:0.911930:0.526921:0.911930:0.512637:0.744263:0.512637:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
origen 0 es::@0.744263:0.542050:0.819013:0.542050:0.819013:0.527766:0.744263:0.527766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.792875:0.540234:0.798447:0.540234:0.798447:0.526442:0.792875:0.526442:0.000000
a:@0.752290:0.575889:0.761549:0.575889:0.761549:0.560454:0.752290:0.560454:0.000000
( ) ( ):@0.743445:0.577806:0.823100:0.579823:0.823100:0.546907:0.743445:0.544889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.754506:0.563325:0.766253:0.563325:0.766253:0.546486:0.754506:0.546486:0.000000:0.000000
:@0.770028:0.563416:0.775771:0.563416:0.775771:0.546275:0.770028:0.546275:0.000000
   :@0.775875:0.571135:0.796986:0.571135:0.796986:0.556851:0.775875:0.556851:0.000000:0.000000:0.000000
1:@0.779466:0.570631:0.793405:0.570631:0.793405:0.558162:0.779466:0.558162:0.000000
b:@0.805517:0.579600:0.814776:0.579600:0.814776:0.564164:0.805517:0.564164:0.000000
y:@0.807373:0.563494:0.815526:0.563494:0.815526:0.546655:0.807373:0.546655:0.000000
:@0.822715:0.565430:0.828458:0.565430:0.828458:0.548289:0.822715:0.548289:0.000000
   1,:@0.828478:0.571135:0.860533:0.571135:0.860533:0.556851:0.828478:0.556851:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.832069:0.570631:0.846008:0.570631:0.846008:0.558162:0.832069:0.558162:0.000000
donde   > 0 y   > 0.:@0.744283:0.596980:0.876163:0.596980:0.876163:0.582696:0.744283:0.582696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.791707:0.596980:0.800124:0.596980:0.800124:0.582948:0.791707:0.582948:0.000000
b:@0.839700:0.596980:0.848117:0.596980:0.848117:0.582948:0.839700:0.582948:0.000000
Competencia :@0.740294:0.145303:0.848854:0.145303:0.848854:0.128356:0.740294:0.128356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.161945:0.837769:0.161945:0.837769:0.144998:0.740294:0.144998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 5 (Ev. 4) Representa lugares geométricos en el plano cartesiano, a partir de su expresión algebraica.:@0.081581:0.965693:0.626925:0.965693:0.626925:0.954266:0.081581:0.954266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c x:@0.301881:0.137446:0.322737:0.137446:0.322737:0.122011:0.301881:0.122011:0.000000:0.000000:0.000000
 :@0.309537:0.137762:0.328480:0.137762:0.328480:0.120621:0.309537:0.120621:0.000000:0.000000:0.000000
a:@0.305750:0.152272:0.315009:0.152272:0.315009:0.136836:0.305750:0.136836:0.000000
:@0.315009:0.152587:0.320752:0.152587:0.320752:0.135446:0.315009:0.135446:0.000000
 2:@0.330250:0.144411:0.350093:0.144411:0.350093:0.130695:0.330250:0.130695:0.000000:0.000000
              ,:@0.350001:0.144966:0.478919:0.144966:0.478919:0.129253:0.350001:0.129253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.353959:0.144966:0.361414:0.144966:0.361414:0.129530:0.353959:0.129530:0.000000
2:@0.361340:0.138902:0.366577:0.138902:0.366577:0.129741:0.361340:0.129741:0.000000
2:@0.370487:0.144411:0.385820:0.144411:0.385820:0.130695:0.370487:0.130695:0.000000
y:@0.389686:0.144966:0.397159:0.144966:0.397159:0.129530:0.389686:0.129530:0.000000
2:@0.397079:0.138902:0.402316:0.138902:0.402316:0.129741:0.397079:0.129741:0.000000
5:@0.406227:0.144411:0.421560:0.144411:0.421560:0.130695:0.406227:0.130695:0.000000
c:@0.425426:0.144966:0.433083:0.144966:0.433083:0.129530:0.425426:0.129530:0.000000
2:@0.433001:0.138902:0.438238:0.138902:0.438238:0.129741:0.433001:0.129741:0.000000
2:@0.442150:0.144411:0.457483:0.144411:0.457483:0.130695:0.442150:0.130695:0.000000
a:@0.461349:0.144966:0.470607:0.144966:0.470607:0.129530:0.461349:0.129530:0.000000
2:@0.470525:0.138902:0.475762:0.138902:0.475762:0.129741:0.470525:0.129741:0.000000
2:@0.271322:0.179886:0.286655:0.179886:0.286655:0.166170:0.271322:0.166170:0.000000
 :@0.286563:0.180440:0.290594:0.180440:0.290594:0.164728:0.286563:0.164728:0.000000
c:@0.331142:0.174735:0.338800:0.174735:0.338800:0.159300:0.331142:0.159300:0.000000
:@0.338800:0.175051:0.344543:0.175051:0.344543:0.157910:0.338800:0.157910:0.000000
a:@0.312687:0.189404:0.321945:0.189404:0.321945:0.173969:0.312687:0.173969:0.000000
:@0.321944:0.189719:0.327687:0.189719:0.327687:0.172578:0.321944:0.172578:0.000000
(:@0.289676:0.190704:0.294554:0.190704:0.294554:0.157788:0.289676:0.157788:0.000000
):@0.349371:0.190704:0.354248:0.190704:0.354248:0.157788:0.349371:0.157788:0.000000
a  :@0.294693:0.175188:0.314151:0.175188:0.314151:0.158350:0.294693:0.158350:0.000000:0.000000:0.000000
:@0.304793:0.175188:0.310536:0.175188:0.310536:0.158047:0.304793:0.158047:0.000000
2:@0.314151:0.174583:0.330878:0.174583:0.330878:0.159620:0.314151:0.159620:0.000000
          (     ).:@0.353400:0.180439:0.507161:0.180439:0.507161:0.164726:0.353400:0.164726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.357351:0.180439:0.364806:0.180439:0.364806:0.165004:0.357351:0.165004:0.000000
2:@0.364739:0.174375:0.369976:0.174375:0.369976:0.165215:0.364739:0.165215:0.000000
2:@0.373887:0.179884:0.389221:0.179884:0.389221:0.166169:0.373887:0.166169:0.000000
y:@0.393086:0.180439:0.400559:0.180439:0.400559:0.165004:0.393086:0.165004:0.000000
2:@0.400477:0.174375:0.405714:0.174375:0.405714:0.165215:0.400477:0.165215:0.000000
5 2:@0.409626:0.179884:0.444158:0.179884:0.444158:0.166169:0.409626:0.166169:0.000000:0.000000:0.000000
a:@0.448870:0.180439:0.458129:0.180439:0.458129:0.165004:0.448870:0.165004:0.000000
2:@0.458040:0.174375:0.463277:0.174375:0.463277:0.165215:0.458040:0.165215:0.000000
2:@0.467189:0.179884:0.482522:0.179884:0.482522:0.166169:0.467189:0.166169:0.000000
c:@0.486387:0.180439:0.494045:0.180439:0.494045:0.165004:0.486387:0.165004:0.000000
2:@0.493963:0.174375:0.499200:0.174375:0.499200:0.165215:0.493963:0.165215:0.000000
Puesto que   >  , entonces,       > 0. Ponemos           y reemplazamos en la :@0.072621:0.213875:0.709982:0.213878:0.709982:0.198165:0.072621:0.198163:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.161086:0.213875:0.170345:0.213875:0.170345:0.198440:0.161086:0.198440:0.000000
c:@0.190887:0.213875:0.198545:0.213875:0.198545:0.198440:0.190887:0.198440:0.000000
a:@0.282813:0.213875:0.292072:0.213875:0.292072:0.198440:0.282813:0.198440:0.000000
2:@0.292136:0.207814:0.297373:0.207814:0.297373:0.198653:0.292136:0.198653:0.000000
2:@0.302153:0.213323:0.317486:0.213323:0.317486:0.199607:0.302153:0.199607:0.000000
c:@0.322290:0.213878:0.329948:0.213878:0.329948:0.198443:0.322290:0.198443:0.000000
2:@0.329981:0.207814:0.335218:0.207814:0.335218:0.198653:0.329981:0.198653:0.000000
b:@0.446979:0.213878:0.456238:0.213878:0.456238:0.198443:0.446979:0.198443:0.000000
2:@0.456275:0.207814:0.461512:0.207814:0.461512:0.198653:0.456275:0.198653:0.000000
5:@0.466290:0.213323:0.481623:0.213323:0.481623:0.199607:0.466290:0.199607:0.000000
a:@0.486428:0.213878:0.495686:0.213878:0.495686:0.198443:0.486428:0.198443:0.000000
2:@0.495720:0.207814:0.500957:0.207814:0.500957:0.198653:0.495720:0.198653:0.000000
2:@0.505737:0.213323:0.521070:0.213323:0.521070:0.199607:0.505737:0.199607:0.000000
c:@0.525874:0.213878:0.533532:0.213878:0.533532:0.198443:0.525874:0.198443:0.000000
2:@0.533565:0.207814:0.538802:0.207814:0.538802:0.198653:0.533565:0.198653:0.000000
última ecuación::@0.072614:0.230520:0.192372:0.230520:0.192372:0.214807:0.072614:0.214807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.072614:0.269004:0.087947:0.269004:0.087947:0.255288:0.072614:0.255288:0.000000
a:@0.088255:0.276737:0.097514:0.276737:0.097514:0.261302:0.088255:0.261302:0.000000
:@0.097514:0.277052:0.103257:0.277052:0.103257:0.259911:0.097514:0.259911:0.000000
b  :@0.088615:0.262521:0.108073:0.262521:0.108073:0.245683:0.088615:0.245683:0.000000:0.000000:0.000000
:@0.098715:0.262521:0.104458:0.262521:0.104458:0.245380:0.098715:0.245380:0.000000
         :@0.106388:0.269564:0.181886:0.269564:0.181886:0.253851:0.106388:0.253851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.110339:0.269564:0.117794:0.269564:0.117794:0.254128:0.110339:0.254128:0.000000
2:@0.117727:0.263500:0.122964:0.263500:0.122964:0.254339:0.117727:0.254339:0.000000
2:@0.126875:0.269009:0.142208:0.269009:0.142208:0.255293:0.126875:0.255293:0.000000
y:@0.146073:0.269564:0.153547:0.269564:0.153547:0.254128:0.146073:0.254128:0.000000
2:@0.153465:0.263500:0.158702:0.263500:0.158702:0.254339:0.153465:0.254339:0.000000
5 2:@0.162614:0.269009:0.197146:0.269009:0.197146:0.255293:0.162614:0.255293:0.000000:0.000000:0.000000
b:@0.197054:0.269564:0.206313:0.269564:0.206313:0.254128:0.197054:0.254128:0.000000
2:@0.206231:0.263500:0.211468:0.263500:0.211468:0.254339:0.206231:0.254339:0.000000
, de donde :@0.211422:0.269564:0.293536:0.269564:0.293536:0.253851:0.211422:0.253851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.294023:0.277877:0.303282:0.277877:0.303282:0.262442:0.294023:0.262442:0.000000
:@0.303282:0.278192:0.309025:0.278192:0.309025:0.261051:0.303282:0.261051:0.000000
x  :@0.296657:0.263661:0.314147:0.263661:0.314147:0.246822:0.296657:0.246822:0.000000:0.000000:0.000000
:@0.304790:0.263661:0.310533:0.263661:0.310533:0.246520:0.304790:0.246520:0.000000
   :@0.312395:0.269564:0.335619:0.269564:0.335619:0.253851:0.312395:0.253851:0.000000:0.000000:0.000000
1:@0.316346:0.269009:0.331679:0.269009:0.331679:0.255293:0.316346:0.255293:0.000000
b:@0.336116:0.277286:0.345374:0.277286:0.345374:0.261850:0.336116:0.261850:0.000000
:@0.345374:0.277601:0.351118:0.277601:0.351118:0.260460:0.345374:0.260460:0.000000
y  :@0.340125:0.260935:0.357635:0.260935:0.357635:0.244097:0.340125:0.244097:0.000000:0.000000:0.000000
:@0.348278:0.260935:0.354021:0.260935:0.354021:0.243794:0.348278:0.243794:0.000000
   1,:@0.354548:0.269564:0.389810:0.269564:0.389810:0.253851:0.354548:0.253851:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.358499:0.269009:0.373832:0.269009:0.373832:0.255293:0.358499:0.255293:0.000000
o también, :@0.072616:0.306619:0.154859:0.306619:0.154859:0.290907:0.072616:0.290907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.162709:0.313339:0.171968:0.313339:0.171968:0.297904:0.162709:0.297904:0.000000
( ) ( ):@0.153864:0.315255:0.236174:0.314509:0.236174:0.281593:0.153864:0.282339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.164925:0.300776:0.176672:0.300776:0.176672:0.283937:0.164925:0.283937:0.000000:0.000000
:@0.180447:0.300867:0.186190:0.300867:0.186190:0.283726:0.180447:0.283726:0.000000
 :@0.186286:0.306614:0.190317:0.306614:0.190317:0.290902:0.186286:0.290902:0.000000
1 :@0.190236:0.306060:0.210079:0.306060:0.210079:0.292344:0.190236:0.292344:0.000000:0.000000
b:@0.218592:0.314286:0.227851:0.314286:0.227851:0.298851:0.218592:0.298851:0.000000
y:@0.220448:0.298181:0.228601:0.298181:0.228601:0.281343:0.220448:0.281343:0.000000
:@0.235789:0.300118:0.241532:0.300118:0.241532:0.282977:0.235789:0.282977:0.000000
   1.:@0.241544:0.306614:0.276806:0.306614:0.276806:0.290902:0.241544:0.290902:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.245495:0.306060:0.260828:0.306060:0.260828:0.292344:0.245495:0.292344:0.000000
Así,     ( ,  )    ( ,  ,  )   :@0.072614:0.344835:0.263892:0.344834:0.263892:0.329121:0.072614:0.329123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.113147:0.344279:0.128480:0.344279:0.128480:0.330564:0.113147:0.330564:0.000000
x y:@0.135291:0.344834:0.157214:0.344834:0.157214:0.329399:0.135291:0.329399:0.000000:0.000000:0.000000
[:@0.164070:0.344544:0.178706:0.344544:0.178706:0.331134:0.164070:0.331134:0.000000
E:@0.182576:0.344834:0.190693:0.344834:0.190693:0.329399:0.182576:0.329399:0.000000
a b:@0.209899:0.344834:0.235411:0.344834:0.235411:0.329399:0.209899:0.329399:0.000000:0.000000:0.000000
a:@0.271814:0.350040:0.281073:0.350040:0.281073:0.334604:0.271814:0.334604:0.000000
( ) ( ):@0.262969:0.351957:0.345279:0.353762:0.345279:0.320846:0.262969:0.319041:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.274030:0.337476:0.285777:0.337476:0.285777:0.320638:0.274030:0.320638:0.000000:0.000000
:@0.289552:0.337567:0.295295:0.337567:0.295295:0.320426:0.289552:0.320426:0.000000
 :@0.295390:0.344834:0.299422:0.344834:0.299422:0.329121:0.295390:0.329121:0.000000
1 :@0.299341:0.344279:0.319184:0.344279:0.319184:0.330564:0.299341:0.330564:0.000000:0.000000
b:@0.327697:0.353539:0.336956:0.353539:0.336956:0.338104:0.327697:0.338104:0.000000
y:@0.329553:0.337433:0.337705:0.337433:0.337705:0.320595:0.329553:0.320595:0.000000
:@0.344894:0.339370:0.350637:0.339370:0.350637:0.322229:0.344894:0.322229:0.000000
   1.:@0.350649:0.344834:0.385911:0.344834:0.385911:0.329121:0.350649:0.329121:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.354600:0.344279:0.369933:0.344279:0.369933:0.330564:0.354600:0.330564:0.000000
A esta última ecuación se la conoce como ecuación cartesiana de la elipse de centro   y :@0.072619:0.378270:0.709893:0.378273:0.709893:0.362560:0.072619:0.362557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
eje transverso al eje  . :@0.072615:0.394915:0.234433:0.394915:0.234433:0.379202:0.072615:0.379202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.218216:0.394915:0.227272:0.394915:0.227272:0.379479:0.218216:0.379479:0.000000
El  conjunto  ( ,  ,  ) puede ser expresado así: :@0.072596:0.428351:0.406371:0.428353:0.406371:0.412641:0.072596:0.412638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.162939:0.428351:0.171057:0.428351:0.171057:0.412915:0.162939:0.412915:0.000000
a b:@0.190287:0.428353:0.215799:0.428353:0.215799:0.412918:0.190287:0.412918:0.000000:0.000000:0.000000
E:@0.072591:0.466366:0.080708:0.466366:0.080708:0.450931:0.072591:0.450931:0.000000
( ,  ,  )       ( ,  )     | :@0.080635:0.466366:0.273958:0.466361:0.273958:0.450648:0.080635:0.450653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.099945:0.466361:0.125457:0.466361:0.125457:0.450926:0.099945:0.450926:0.000000:0.000000:0.000000
5:@0.134127:0.465806:0.149460:0.465806:0.149460:0.452091:0.134127:0.452091:0.000000
5:@0.153563:0.468167:0.157649:0.468167:0.157649:0.444886:0.153563:0.444886:0.000000
5:@0.170649:0.465806:0.185983:0.465806:0.185983:0.452091:0.170649:0.452091:0.000000
x y:@0.194634:0.466361:0.216557:0.466361:0.216557:0.450926:0.194634:0.450926:0.000000:0.000000:0.000000
[:@0.225254:0.466071:0.239890:0.466071:0.239890:0.452661:0.225254:0.452661:0.000000
R:@0.243760:0.465501:0.257050:0.465501:0.257050:0.452604:0.243760:0.452604:0.000000
2:@0.256949:0.460297:0.262186:0.460297:0.262186:0.451137:0.256949:0.451137:0.000000
a:@0.281864:0.474363:0.291123:0.474363:0.291123:0.458928:0.281864:0.458928:0.000000
( ):@0.273019:0.476279:0.299986:0.476279:0.299986:0.443363:0.273019:0.443363:0.000000:0.000000:0.000000
x :@0.284080:0.461800:0.295827:0.461800:0.295827:0.444961:0.284080:0.444961:0.000000:0.000000
:@0.299602:0.461890:0.305345:0.461890:0.305345:0.444749:0.299602:0.444749:0.000000
   :@0.305442:0.466361:0.328664:0.466361:0.328664:0.450648:0.305442:0.450648:0.000000:0.000000:0.000000
1:@0.309392:0.465806:0.324725:0.465806:0.324725:0.452091:0.309392:0.452091:0.000000
b:@0.337188:0.473077:0.346447:0.473077:0.346447:0.457642:0.337188:0.457642:0.000000
( ):@0.327804:0.473300:0.354771:0.473300:0.354771:0.440384:0.327804:0.440384:0.000000:0.000000:0.000000
y:@0.339044:0.456971:0.347197:0.456971:0.347197:0.440132:0.339044:0.440132:0.000000
:@0.354386:0.458907:0.360129:0.458907:0.360129:0.441766:0.354386:0.441766:0.000000
   1 .:@0.360140:0.466361:0.400327:0.466361:0.400327:0.450648:0.360140:0.450648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.364091:0.465806:0.379425:0.465806:0.379425:0.452091:0.364091:0.452091:0.000000
6:@0.392405:0.469648:0.396491:0.469648:0.396491:0.446366:0.392405:0.446366:0.000000
Dados  ,     :@0.072615:0.499800:0.179758:0.499800:0.179758:0.484087:0.072615:0.484087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.126677:0.499800:0.154748:0.499800:0.154748:0.484364:0.126677:0.484364:0.000000:0.000000:0.000000
[:@0.160825:0.499510:0.175461:0.499510:0.175461:0.486100:0.160825:0.486100:0.000000
R:@0.181617:0.498940:0.194907:0.498940:0.194907:0.486042:0.181617:0.486042:0.000000
1:@0.195191:0.493412:0.204131:0.493412:0.204131:0.485416:0.195191:0.485416:0.000000
, las coordenadas de los focos   y   se obtienen de la ecuación  :@0.204293:0.499800:0.709905:0.499800:0.709905:0.484087:0.204293:0.484087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.450773:0.502972:0.456010:0.502972:0.456010:0.493812:0.450773:0.493812:0.000000
2:@0.484836:0.502972:0.490073:0.502972:0.490073:0.493812:0.484836:0.493812:0.000000
c:@0.072627:0.516442:0.080285:0.516442:0.080285:0.501006:0.072627:0.501006:0.000000
2:@0.080205:0.510378:0.085442:0.510378:0.085442:0.501217:0.080205:0.501217:0.000000
        . Nota que   >  .:@0.085395:0.516442:0.279483:0.516442:0.279483:0.500729:0.085395:0.500729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.089353:0.515887:0.104686:0.515887:0.104686:0.502171:0.089353:0.502171:0.000000
a:@0.108552:0.516442:0.117810:0.516442:0.117810:0.501006:0.108552:0.501006:0.000000
2:@0.117730:0.510378:0.122967:0.510378:0.122967:0.501217:0.117730:0.501217:0.000000
2:@0.126877:0.515887:0.142210:0.515887:0.142210:0.502171:0.126877:0.502171:0.000000
b:@0.146076:0.516442:0.155335:0.516442:0.155335:0.501006:0.146076:0.501006:0.000000
2:@0.155254:0.510378:0.160491:0.510378:0.160491:0.501217:0.155254:0.501217:0.000000
a:@0.239116:0.516442:0.248375:0.516442:0.248375:0.501006:0.239116:0.501006:0.000000
b:@0.267095:0.516442:0.276354:0.516442:0.276354:0.501006:0.267095:0.501006:0.000000
Definición:@0.072604:0.549878:0.150572:0.549878:0.150572:0.533208:0.072604:0.533208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. La excentricidad de la elipse se designa con   y se define como::@0.150467:0.549878:0.616115:0.549878:0.616115:0.534165:0.150467:0.534165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.477159:0.549878:0.484945:0.549878:0.484945:0.534442:0.477159:0.534442:0.000000
e:@0.072604:0.594866:0.080390:0.594866:0.080390:0.579431:0.072604:0.579431:0.000000
       :@0.080317:0.594866:0.138947:0.594864:0.138947:0.579151:0.080317:0.579153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.084274:0.594311:0.099608:0.594311:0.099608:0.580596:0.084274:0.580596:0.000000
a:@0.103876:0.602284:0.113135:0.602284:0.113135:0.586849:0.103876:0.586849:0.000000
c :@0.104235:0.588068:0.116203:0.588068:0.116203:0.571230:0.104235:0.571230:0.000000:0.000000
5:@0.119675:0.594309:0.135008:0.594309:0.135008:0.580593:0.119675:0.580593:0.000000
a:@0.168116:0.600620:0.177375:0.600620:0.177375:0.585185:0.168116:0.585185:0.000000
a:@0.146939:0.586408:0.157040:0.586408:0.157040:0.569569:0.146939:0.569569:0.000000
 :@0.157040:0.586408:0.167181:0.586408:0.167181:0.569267:0.157040:0.569267:0.000000:0.000000
2 :@0.167181:0.585803:0.188928:0.585803:0.188928:0.570840:0.167181:0.570840:0.000000:0.000000
b:@0.188928:0.586408:0.199028:0.586408:0.199028:0.569569:0.188928:0.569569:0.000000
:@0.199028:0.586408:0.204771:0.586408:0.204771:0.569267:0.199028:0.569267:0.000000
5     2 :@0.204169:0.594638:0.271705:0.594644:0.271705:0.579682:0.204169:0.579675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.240975:0.594934:0.249958:0.594934:0.249958:0.579222:0.240975:0.579222:0.000000
a:@0.277704:0.599469:0.286963:0.599469:0.286963:0.584034:0.277704:0.584034:0.000000
( ):@0.268857:0.600662:0.295824:0.600662:0.295824:0.567745:0.268857:0.567745:0.000000:0.000000:0.000000
b :@0.278245:0.586905:0.291960:0.586905:0.291960:0.570066:0.278245:0.570066:0.000000:0.000000
:@0.294872:0.587237:0.300615:0.587237:0.300615:0.570096:0.294872:0.570096:0.000000
.:@0.302875:0.594864:0.306078:0.594864:0.306078:0.579151:0.302875:0.579151:0.000000
Como       se sigue que         1; es decir que la elipse es una sección cónica que :@0.072615:0.631269:0.709800:0.631269:0.709800:0.615556:0.072615:0.615556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.122130:0.631269:0.131389:0.631269:0.131389:0.615834:0.122130:0.615834:0.000000
.:@0.135844:0.630714:0.151177:0.630714:0.151177:0.616999:0.135844:0.616999:0.000000
c,:@0.155631:0.631269:0.166436:0.631269:0.166436:0.615834:0.155631:0.615834:0.000000:0.000000
e:@0.268173:0.631269:0.275960:0.631269:0.275960:0.615834:0.268173:0.615834:0.000000
5:@0.280414:0.630714:0.295747:0.630714:0.295747:0.616999:0.280414:0.616999:0.000000
a:@0.300603:0.637014:0.309862:0.637014:0.309862:0.621579:0.300603:0.621579:0.000000
c :@0.300963:0.622798:0.312931:0.622798:0.312931:0.605959:0.300963:0.605959:0.000000:0.000000
,:@0.316989:0.630714:0.332322:0.630714:0.332322:0.616999:0.316989:0.616999:0.000000
tiene excentricidad menor que 1. En la Figura 2.30. se muestran el conjunto  ( ,  ,  ), los :@0.072614:0.647911:0.709920:0.647911:0.709920:0.632198:0.072614:0.632198:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.620672:0.647911:0.628789:0.647911:0.628789:0.632475:0.620672:0.632475:0.000000
a b:@0.648053:0.647911:0.673621:0.647911:0.673621:0.632475:0.648053:0.632475:0.000000:0.000000:0.000000
focos   y  , así y un punto     (x,  ) de la elipse.:@0.072606:0.664553:0.425375:0.664553:0.425375:0.648840:0.072606:0.648840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.123651:0.667725:0.128888:0.667725:0.128888:0.658564:0.123651:0.658564:0.000000
2:@0.153042:0.667725:0.158279:0.667725:0.158279:0.658564:0.153042:0.658564:0.000000
5:@0.286316:0.663998:0.301649:0.663998:0.301649:0.650282:0.286316:0.650282:0.000000
y:@0.325192:0.664553:0.332665:0.664553:0.332665:0.649117:0.325192:0.649117:0.000000
Con la ecuación de la elipse podemos determinar las intersecciones de la elipse :@0.072607:0.697989:0.661910:0.697989:0.661910:0.682276:0.072607:0.682276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con los ejes coordenados, del siguiente modo::@0.072607:0.714631:0.408849:0.714631:0.408849:0.698918:0.072607:0.698918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si     0, obtenemos :@0.072607:0.750300:0.221993:0.750300:0.221993:0.734587:0.072607:0.734587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.087112:0.750300:0.094567:0.750300:0.094567:0.734864:0.087112:0.734864:0.000000
5:@0.098451:0.749745:0.113784:0.749745:0.113784:0.736029:0.098451:0.736029:0.000000
b:@0.230436:0.759357:0.239695:0.759357:0.239695:0.743922:0.230436:0.743922:0.000000
( ):@0.221052:0.759580:0.248019:0.759580:0.248019:0.726664:0.221052:0.726664:0.000000:0.000000:0.000000
y:@0.232292:0.743251:0.240445:0.743251:0.240445:0.726412:0.232292:0.726412:0.000000
:@0.247634:0.745187:0.253377:0.745187:0.253377:0.728046:0.247634:0.728046:0.000000
   1, de donde     :@0.253388:0.750303:0.398024:0.750303:0.398024:0.734591:0.253388:0.734591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.257338:0.749749:0.272671:0.749749:0.272671:0.736033:0.257338:0.736033:0.000000
y:@0.367395:0.750303:0.374868:0.750303:0.374868:0.734868:0.367395:0.734868:0.000000
5 6:@0.378752:0.749749:0.413284:0.749749:0.413284:0.736033:0.378752:0.736033:0.000000:0.000000:0.000000
b:@0.413192:0.750303:0.422451:0.750303:0.422451:0.734868:0.413192:0.734868:0.000000
; cuando     0,:@0.422377:0.750303:0.531606:0.750303:0.531606:0.734591:0.422377:0.734591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.488938:0.750303:0.496411:0.750303:0.496411:0.734868:0.488938:0.734868:0.000000
5:@0.500295:0.749749:0.515628:0.749749:0.515628:0.736033:0.500295:0.736033:0.000000
obtenemos :@0.072621:0.789273:0.160475:0.789273:0.160475:0.773560:0.072621:0.773560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.167908:0.793728:0.177167:0.793728:0.177167:0.778293:0.167908:0.778293:0.000000
( ):@0.159063:0.795645:0.186030:0.795645:0.186030:0.762728:0.159063:0.762728:0.000000:0.000000:0.000000
x :@0.170122:0.781165:0.181870:0.781165:0.181870:0.764327:0.170122:0.764327:0.000000:0.000000
:@0.185645:0.781256:0.191388:0.781256:0.191388:0.764115:0.185645:0.764115:0.000000
   1, con lo que      :@0.191433:0.789278:0.342260:0.789278:0.342260:0.773565:0.191433:0.773565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.194929:0.788723:0.210262:0.788723:0.210262:0.775008:0.194929:0.775008:0.000000
x:@0.308704:0.789278:0.316159:0.789278:0.316159:0.773843:0.308704:0.773843:0.000000
5 6:@0.319546:0.788723:0.357060:0.788723:0.357060:0.775008:0.319546:0.775008:0.000000:0.000000:0.000000
a:@0.356912:0.789278:0.366171:0.789278:0.366171:0.773843:0.356912:0.773843:0.000000
. Así, la intersección de la elipse con el eje :@0.366061:0.789278:0.662615:0.789278:0.662615:0.773565:0.366061:0.773565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.072631:0.805920:0.081687:0.805920:0.081687:0.790485:0.072631:0.790485:0.000000
 es conformada por los puntos     (:@0.081650:0.805920:0.351765:0.805920:0.351765:0.790207:0.081650:0.790207:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.317580:0.809092:0.322816:0.809092:0.322816:0.799932:0.317580:0.799932:0.000000
5 2:@0.327191:0.805365:0.367062:0.805365:0.367062:0.791650:0.327191:0.791650:0.000000:0.000000:0.000000
a:@0.367006:0.805920:0.376265:0.805920:0.376265:0.790485:0.367006:0.790485:0.000000
, 0) y     ( , 0), que se conocen como :@0.376228:0.805920:0.662575:0.805920:0.662575:0.790207:0.376228:0.790207:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.421601:0.809092:0.426837:0.809092:0.426837:0.799932:0.421601:0.799932:0.000000
5:@0.431214:0.805365:0.446547:0.805365:0.446547:0.791650:0.431214:0.791650:0.000000
a:@0.455751:0.805920:0.465010:0.805920:0.465010:0.790485:0.455751:0.790485:0.000000
vértices de la elipse. La intersección de la elipse con el eje   es conformada por los :@0.072641:0.822562:0.662568:0.822562:0.662568:0.806849:0.072641:0.806849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Y:@0.485829:0.822562:0.494738:0.822562:0.494738:0.807126:0.485829:0.807126:0.000000
puntos     (0, :@0.072641:0.839204:0.184637:0.839204:0.184637:0.823491:0.072641:0.823491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.135897:0.842376:0.141133:0.842376:0.141133:0.833215:0.135897:0.833215:0.000000
5:@0.144804:0.838649:0.160137:0.838649:0.160137:0.824933:0.144804:0.824933:0.000000
2:@0.184288:0.838649:0.199621:0.838649:0.199621:0.824933:0.184288:0.824933:0.000000
b:@0.199529:0.839204:0.208788:0.839204:0.208788:0.823768:0.199529:0.823768:0.000000
) y     (0,  ). La distancia  ( ,  )   ||     ||   2  se llama eje :@0.208714:0.839204:0.662525:0.839204:0.662525:0.823491:0.208714:0.823491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.236984:0.842376:0.242221:0.842376:0.242221:0.833215:0.236984:0.833215:0.000000
5:@0.245892:0.838649:0.261225:0.838649:0.261225:0.824933:0.245892:0.824933:0.000000
b:@0.285375:0.839204:0.294634:0.839204:0.294634:0.823768:0.285375:0.823768:0.000000
d:@0.394383:0.839204:0.403642:0.839204:0.403642:0.823768:0.394383:0.823768:0.000000
1:@0.415556:0.842376:0.420793:0.842376:0.420793:0.833215:0.415556:0.833215:0.000000
2:@0.434747:0.842376:0.439984:0.842376:0.439984:0.833215:0.434747:0.833215:0.000000
5:@0.448442:0.838649:0.463775:0.838649:0.463775:0.824933:0.448442:0.824933:0.000000
1:@0.482212:0.842376:0.487449:0.842376:0.487449:0.833215:0.482212:0.833215:0.000000
2:@0.491121:0.838649:0.506455:0.838649:0.506455:0.824933:0.491121:0.824933:0.000000
2:@0.517238:0.842376:0.522475:0.842376:0.522475:0.833215:0.517238:0.833215:0.000000
5:@0.533784:0.838649:0.549118:0.838649:0.549118:0.824933:0.533784:0.824933:0.000000
a:@0.561635:0.839204:0.570893:0.839204:0.570893:0.823768:0.561635:0.823768:0.000000
mayor de la elipse; y la distancia  ( ,  )   ||     ||   2  se llama eje menor de :@0.072591:0.855845:0.662591:0.855845:0.662591:0.840133:0.072591:0.840133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.309271:0.855845:0.318530:0.855845:0.318530:0.840410:0.309271:0.840410:0.000000
1:@0.331295:0.859018:0.336531:0.859018:0.336531:0.849857:0.331295:0.849857:0.000000
2:@0.351902:0.859018:0.357139:0.859018:0.357139:0.849857:0.351902:0.849857:0.000000
5:@0.366168:0.855291:0.381501:0.855291:0.381501:0.841575:0.366168:0.841575:0.000000
1:@0.401354:0.859018:0.406591:0.859018:0.406591:0.849857:0.401354:0.849857:0.000000
2:@0.410832:0.855291:0.426166:0.855291:0.426166:0.841575:0.410832:0.841575:0.000000
2:@0.438365:0.859018:0.443601:0.859018:0.443601:0.849857:0.438365:0.849857:0.000000
5:@0.455482:0.855291:0.470815:0.855291:0.470815:0.841575:0.455482:0.841575:0.000000
b:@0.483902:0.855845:0.493161:0.855845:0.493161:0.840410:0.483902:0.840410:0.000000
la elipse.:@0.072611:0.872487:0.133881:0.872487:0.133881:0.856775:0.072611:0.856775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En los ejercicios se propone obtener la ecuación cartesiana de la elipse  ( ,  ,  ), :@0.072611:0.905923:0.662475:0.905925:0.662475:0.890213:0.072611:0.890211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.596334:0.905923:0.604452:0.905923:0.604452:0.890488:0.596334:0.890488:0.000000
a b:@0.624326:0.905925:0.650409:0.905925:0.650409:0.890490:0.624326:0.890490:0.000000:0.000000:0.000000
donde  ,  ,     :@0.072624:0.922567:0.186008:0.922567:0.186008:0.906855:0.072624:0.906855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.124422:0.922567:0.163887:0.922567:0.163887:0.907132:0.124422:0.907132:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.167428:0.922277:0.182064:0.922277:0.182064:0.908867:0.167428:0.908867:0.000000
R:@0.185566:0.921707:0.198856:0.921707:0.198856:0.908810:0.185566:0.908810:0.000000
1:@0.198771:0.916180:0.207710:0.916180:0.207710:0.908184:0.198771:0.908184:0.000000
, y los puntos     (0,  c)  y     (0, c) fijos están localizados en :@0.207656:0.922567:0.662608:0.922567:0.662608:0.906855:0.207656:0.906855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.313336:0.925740:0.318573:0.925740:0.318573:0.916579:0.313336:0.916579:0.000000
5:@0.322114:0.922013:0.337448:0.922013:0.337448:0.908297:0.322114:0.908297:0.000000
2:@0.361377:0.922013:0.376710:0.922013:0.376710:0.908297:0.361377:0.908297:0.000000
1:@0.416632:0.925740:0.421869:0.925740:0.421869:0.916579:0.416632:0.916579:0.000000
5:@0.425413:0.922013:0.440746:0.922013:0.440746:0.908297:0.425413:0.908297:0.000000
el eje  .:@0.072601:0.939209:0.126755:0.939209:0.126755:0.923496:0.072601:0.923496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Y:@0.114717:0.939209:0.123626:0.939209:0.123626:0.923774:0.114717:0.923774:0.000000
Figura 2.34:@0.869054:0.940006:0.926913:0.940006:0.926913:0.928578:0.869054:0.928578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.791382:0.916479:0.802534:0.916479:0.802534:0.906504:0.791382:0.906504:0.000000
b:@0.802532:0.916883:0.809922:0.916883:0.809922:0.905455:0.802532:0.905455:0.000000
b:@0.804205:0.829226:0.811595:0.829226:0.811595:0.817798:0.804205:0.817798:0.000000
a:@0.893778:0.880462:0.899856:0.880462:0.899856:0.869035:0.893778:0.869035:0.000000
2:@0.716614:0.880059:0.727765:0.880059:0.727765:0.870084:0.716614:0.870084:0.000000
a:@0.727765:0.880462:0.733843:0.880462:0.733843:0.869035:0.727765:0.869035:0.000000
y:@0.798477:0.814506:0.805472:0.814506:0.805472:0.800936:0.798477:0.800936:0.000000
x:@0.912635:0.883637:0.919455:0.883637:0.919455:0.870067:0.912635:0.870067:0.000000
x:@0.855742:0.836389:0.862757:0.836389:0.862757:0.821866:0.855742:0.821866:0.000000
:@0.857993:0.836898:0.863761:0.836898:0.863761:0.822623:0.857993:0.822623:0.000000
F:@0.744288:0.883466:0.750870:0.883466:0.750870:0.870837:0.744288:0.870837:0.000000
:@0.747029:0.881639:0.752044:0.881639:0.752044:0.869226:0.747029:0.869226:0.000000
1:@0.750839:0.886061:0.755124:0.886061:0.755124:0.878566:0.750839:0.878566:0.000000
   (:@0.755123:0.883466:0.777104:0.883466:0.777104:0.870610:0.755123:0.870610:0.000000:0.000000:0.000000:0.000000
5 2:@0.757849:0.883012:0.789649:0.883012:0.789649:0.871790:0.757849:0.871790:0.000000:0.000000:0.000000
c:@0.789649:0.883466:0.795915:0.883466:0.795915:0.870837:0.789649:0.870837:0.000000
, 0):@0.795915:0.883466:0.812594:0.883466:0.812594:0.870610:0.795915:0.870610:0.000000:0.000000:0.000000:0.000000
F:@0.828935:0.883375:0.835516:0.883375:0.835516:0.870746:0.828935:0.870746:0.000000
:@0.831676:0.881548:0.836691:0.881548:0.836691:0.869135:0.831676:0.869135:0.000000
2:@0.835483:0.885974:0.839767:0.885974:0.839767:0.878479:0.835483:0.878479:0.000000
   ( , 0):@0.839767:0.883379:0.886424:0.883379:0.886424:0.870523:0.839767:0.870523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.843065:0.882925:0.855610:0.882925:0.855610:0.871703:0.843065:0.871703:0.000000
c:@0.862899:0.883379:0.869165:0.883379:0.869165:0.870750:0.862899:0.870750:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000