133:@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:@0.538113:0.043660:0.926913:0.043660:0.926913:0.024915:0.538113:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2. Considera la hipérbola::@0.073089:0.136836:0.277389:0.136836:0.277389:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , 2, 3) ( , ) | :@0.367388:0.170815:0.560102:0.170815:0.560102:0.155102:0.367388:0.155102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.420292:0.170260:0.435625:0.170260:0.435625:0.156544:0.420292:0.156544:0.000000 5:@0.439705:0.173898:0.443791:0.173898:0.443791:0.150616:0.439705:0.150616:0.000000 5:@0.456792:0.170260:0.472125:0.170260:0.472125:0.156544:0.456792:0.156544:0.000000 x y:@0.480777:0.170815:0.502700:0.170815:0.502700:0.155379:0.480777:0.155379:0.000000:0.000000:0.000000 [:@0.511396:0.170525:0.526032:0.170525:0.526032:0.157115:0.511396:0.157115:0.000000 R:@0.529902:0.169955:0.543192:0.169955:0.543192:0.157057:0.529902:0.157057:0.000000 2:@0.543093:0.164751:0.548330:0.164751:0.548330:0.155590:0.543093:0.155590:0.000000 x:@0.567493:0.161485:0.574948:0.161485:0.574948:0.146050:0.567493:0.146050:0.000000 2:@0.566591:0.179472:0.575574:0.179472:0.575574:0.163759:0.566591:0.163759:0.000000 1 2:@0.560073:0.177087:0.582443:0.177087:0.582443:0.149236:0.560073:0.149236:0.000000:0.000000:0.000000 :@0.582457:0.165050:0.587721:0.165050:0.587721:0.149338:0.582457:0.149338:0.000000 :@0.588534:0.170815:0.611758:0.170815:0.611758:0.155102:0.588534:0.155102:0.000000:0.000000:0.000000 2:@0.592485:0.170260:0.607818:0.170260:0.607818:0.156544:0.592485:0.156544:0.000000 y:@0.619164:0.163548:0.626637:0.163548:0.626637:0.148112:0.619164:0.148112:0.000000 3:@0.618262:0.181535:0.627245:0.181535:0.627245:0.165822:0.618262:0.165822:0.000000 1 2:@0.611744:0.179150:0.634114:0.179150:0.634114:0.151298:0.611744:0.151298:0.000000:0.000000:0.000000 :@0.634129:0.167113:0.639394:0.167113:0.639394:0.151400:0.634129:0.151400:0.000000 1 .:@0.640192:0.170815:0.679043:0.170815:0.679043:0.155102:0.640192:0.155102:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.643774:0.170260:0.659108:0.170260:0.659108:0.156544:0.643774:0.156544:0.000000 a.:@0.104626:0.205638:0.116112:0.205638:0.116112:0.189925:0.104626:0.189925:0.000000:0.000000 Verifica:@0.116031:0.205639:0.190316:0.205639:0.190316:0.188969:0.116031:0.188969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cuál de los puntos 5 , :@0.190216:0.205639:0.390474:0.205639:0.390474:0.189926:0.190216:0.189926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.330762:0.206729:0.334849:0.206729:0.334849:0.183447:0.330762:0.183447:0.000000 2:@0.371202:0.205084:0.386535:0.205084:0.386535:0.191368:0.371202:0.191368:0.000000 3:@0.393329:0.199167:0.402311:0.199167:0.402311:0.183455:0.393329:0.183455:0.000000 2:@0.392684:0.213008:0.401667:0.213008:0.401667:0.197295:0.392684:0.197295:0.000000 2:@0.405282:0.209618:0.409368:0.209618:0.409368:0.186336:0.405282:0.186336:0.000000 , ( 4, 0):@0.410001:0.205639:0.466896:0.205639:0.466896:0.189926:0.410001:0.189926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.421872:0.205084:0.437205:0.205084:0.437205:0.191368:0.421872:0.191368:0.000000 ( 6, 6 2) pertenecen a ( , 2, 3).:@0.133330:0.236576:0.391650:0.236576:0.391650:0.220864:0.133330:0.220864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 2:@0.138129:0.236022:0.184681:0.236022:0.184681:0.222306:0.138129:0.222306:0.000000:0.000000:0.000000 b.:@0.104633:0.267514:0.117592:0.267514:0.117592:0.251801:0.104633:0.251801:0.000000:0.000000 Verifica:@0.117504:0.267514:0.190316:0.267514:0.190316:0.250844:0.117504:0.250844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que los puntos (2, 5), ( 1, 3),:@0.190216:0.267514:0.416055:0.267514:0.416055:0.251801:0.190216:0.251801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 2:@0.352679:0.266959:0.399231:0.266959:0.399231:0.253243:0.352679:0.253243:0.000000:0.000000:0.000000 :@0.104633:0.298450:0.108664:0.298450:0.108664:0.282737:0.104633:0.282737:0.000000 (0, 4) no pertenecen a ( , 2, 3).:@0.133330:0.298450:0.362942:0.298450:0.362942:0.282737:0.133330:0.282737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c.:@0.104633:0.329387:0.115585:0.329387:0.115585:0.313675:0.104633:0.313675:0.000000:0.000000 Obtén:@0.115313:0.329387:0.182292:0.329387:0.182292:0.312718:0.115313:0.312718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los focos, los vértices, la excentricidad y las asíntotas. :@0.182020:0.329387:0.556823:0.329387:0.556823:0.313675:0.182020:0.313675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Representa:@0.556203:0.329387:0.640219:0.329387:0.640219:0.312718:0.556203:0.312718:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en tu cuaderno gráficamente ( , 2, 3).:@0.639937:0.329387:0.919763:0.329387:0.919763:0.313675:0.639937:0.313675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3. Considera la hipérbola::@0.073089:0.360323:0.277389:0.360323:0.277389:0.343654:0.073089:0.343654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , ) |:@0.383951:0.396681:0.527703:0.396681:0.527703:0.380968:0.383951:0.380968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.387902:0.396126:0.403235:0.396126:0.403235:0.382410:0.387902:0.382410:0.000000 5:@0.407315:0.400269:0.411401:0.400269:0.411401:0.376987:0.407315:0.376987:0.000000 5:@0.428351:0.396126:0.443684:0.396126:0.443684:0.382410:0.428351:0.382410:0.000000 x y:@0.452336:0.396681:0.474259:0.396681:0.474259:0.381246:0.452336:0.381246:0.000000:0.000000:0.000000 [:@0.482957:0.396391:0.497593:0.396391:0.497593:0.382981:0.482957:0.382981:0.000000 R:@0.501463:0.395821:0.514753:0.395821:0.514753:0.382924:0.501463:0.382924:0.000000 2:@0.514654:0.390617:0.519891:0.390617:0.519891:0.381456:0.514654:0.381456:0.000000 5:@0.543406:0.406808:0.551573:0.406808:0.551573:0.392524:0.543406:0.392524:0.000000 X:@0.540734:0.390165:0.548967:0.390165:0.548967:0.376133:0.540734:0.376133:0.000000 1 2 1 2:@0.528010:0.402992:0.621738:0.402690:0.621738:0.374839:0.528010:0.375141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.560113:0.389843:0.565378:0.389843:0.565378:0.374130:0.560113:0.374130:0.000000 :@0.565532:0.396681:0.588755:0.396681:0.588755:0.380968:0.565532:0.380968:0.000000:0.000000:0.000000 2:@0.569483:0.396126:0.584816:0.396126:0.584816:0.382410:0.569483:0.382410:0.000000 3:@0.604463:0.406187:0.613446:0.406187:0.613446:0.390474:0.604463:0.390474:0.000000 y:@0.601794:0.387673:0.609268:0.387673:0.609268:0.372237:0.601794:0.372237:0.000000 :@0.621172:0.388906:0.626436:0.388906:0.626436:0.373193:0.621172:0.373193:0.000000 1 .:@0.626589:0.396681:0.662458:0.396681:0.662458:0.380968:0.626589:0.380968:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.630171:0.396126:0.645505:0.396126:0.645505:0.382410:0.630171:0.382410:0.000000 6:@0.654536:0.400566:0.658622:0.400566:0.658622:0.377284:0.654536:0.377284:0.000000 a.:@0.104633:0.427617:0.116064:0.427617:0.116064:0.411904:0.104633:0.411904:0.000000:0.000000 Obtén:@0.115921:0.427617:0.182808:0.427617:0.182808:0.410947:0.115921:0.410947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las coordenadas de los focos y :@0.182664:0.427617:0.408231:0.427617:0.408231:0.411904:0.182664:0.411904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 calcula:@0.407896:0.427617:0.460191:0.427617:0.460191:0.410947:0.407896:0.410947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la excentricidad. :@0.460025:0.427617:0.584198:0.427617:0.584198:0.411904:0.460025:0.411904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Compara:@0.583961:0.427617:0.653257:0.427617:0.653257:0.410947:0.583961:0.410947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tu resultado:@0.653099:0.427617:0.743618:0.427617:0.743618:0.411904:0.653099:0.411904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con ( 2 2 , 0), (2 2 , 0), :@0.133330:0.465420:0.397265:0.465420:0.397265:0.449708:0.133330:0.449708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.173190:0.468593:0.178427:0.468593:0.178427:0.459432:0.173190:0.459432:0.000000 5 2:@0.182338:0.464866:0.221656:0.464866:0.221656:0.451150:0.182338:0.451150:0.000000:0.000000:0.000000 2:@0.291294:0.468593:0.296531:0.468593:0.296531:0.459432:0.291294:0.459432:0.000000 5:@0.300442:0.464866:0.315776:0.464866:0.315776:0.451150:0.300442:0.451150:0.000000 e:@0.385521:0.465420:0.393307:0.465420:0.393307:0.449985:0.385521:0.449985:0.000000 5:@0.397191:0.464866:0.412524:0.464866:0.412524:0.451150:0.397191:0.451150:0.000000 10:@0.438249:0.457456:0.456215:0.457456:0.456215:0.441744:0.438249:0.441744:0.000000:0.000000 2:@0.415874:0.457609:0.424857:0.457609:0.424857:0.441896:0.415874:0.441896:0.000000 5:@0.430655:0.473432:0.439638:0.473432:0.439638:0.457720:0.430655:0.457720:0.000000 .:@0.458763:0.465420:0.461966:0.465420:0.461966:0.449708:0.458763:0.449708:0.000000 b.:@0.104633:0.496358:0.117591:0.496358:0.117591:0.480645:0.104633:0.480645:0.000000:0.000000 Demuestra:@0.117504:0.496358:0.218608:0.496358:0.218608:0.479688:0.117504:0.479688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que las rectas asíntotas a esta hipérbola están definidas como::@0.218503:0.496358:0.671771:0.496358:0.671771:0.480645:0.218503:0.480645:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.104633:0.535109:0.108664:0.535109:0.108664:0.519397:0.104633:0.519397:0.000000 R:@0.133331:0.535109:0.142277:0.535109:0.142277:0.519674:0.133331:0.519674:0.000000 1:@0.142210:0.538282:0.147447:0.538282:0.147447:0.529121:0.142210:0.529121:0.000000 ( , ) | :@0.147399:0.535109:0.274890:0.535109:0.274890:0.519397:0.147399:0.519397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.151357:0.534555:0.166690:0.534555:0.166690:0.520839:0.151357:0.520839:0.000000 5:@0.170763:0.539742:0.174850:0.539742:0.174850:0.516461:0.170763:0.516461:0.000000 x y:@0.184231:0.535109:0.206154:0.535109:0.206154:0.519674:0.184231:0.519674:0.000000:0.000000:0.000000 [:@0.214847:0.534819:0.229483:0.534819:0.229483:0.521409:0.214847:0.521409:0.000000 R:@0.233353:0.534250:0.246643:0.534250:0.246643:0.521352:0.233353:0.521352:0.000000 2:@0.246544:0.529045:0.251781:0.529045:0.251781:0.519885:0.246544:0.519885:0.000000 y:@0.263459:0.535109:0.270932:0.535109:0.270932:0.519674:0.263459:0.519674:0.000000 5:@0.274816:0.534555:0.290149:0.534555:0.290149:0.520839:0.274816:0.520839:0.000000 3:@0.301102:0.526198:0.310084:0.526198:0.310084:0.510486:0.301102:0.510486:0.000000 5:@0.301102:0.543884:0.310084:0.543884:0.310084:0.528171:0.301102:0.528171:0.000000 ,:@0.314015:0.535109:0.336758:0.535109:0.336758:0.519397:0.314015:0.519397:0.000000:0.000000:0.000000 x :@0.317966:0.535109:0.328661:0.535109:0.328661:0.519674:0.317966:0.519674:0.000000:0.000000 6:@0.328823:0.537331:0.332909:0.537331:0.332909:0.514049:0.328823:0.514049:0.000000 R:@0.133330:0.573630:0.142276:0.573630:0.142276:0.558195:0.133330:0.558195:0.000000 2:@0.142210:0.576802:0.147447:0.576802:0.147447:0.567642:0.142210:0.567642:0.000000 ( , ) | :@0.147399:0.573630:0.313287:0.573630:0.313287:0.557917:0.147399:0.557917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.151357:0.573075:0.166690:0.573075:0.166690:0.559360:0.151357:0.559360:0.000000 5:@0.170763:0.578262:0.174850:0.578262:0.174850:0.554980:0.170763:0.554980:0.000000 x y:@0.184231:0.573630:0.206154:0.573630:0.206154:0.558195:0.184231:0.558195:0.000000:0.000000:0.000000 [:@0.214847:0.573340:0.229483:0.573340:0.229483:0.559930:0.214847:0.559930:0.000000 R:@0.233353:0.572770:0.246643:0.572770:0.246643:0.559873:0.233353:0.559873:0.000000 2:@0.246543:0.567566:0.251779:0.567566:0.251779:0.558406:0.246543:0.558406:0.000000 y:@0.263459:0.573630:0.270932:0.573630:0.270932:0.558195:0.263459:0.558195:0.000000 5 2:@0.274816:0.573075:0.309348:0.573075:0.309348:0.559360:0.274816:0.559360:0.000000:0.000000:0.000000 3:@0.324245:0.564949:0.333227:0.564949:0.333227:0.549236:0.324245:0.549236:0.000000 5:@0.324245:0.582636:0.333227:0.582636:0.333227:0.566923:0.324245:0.566923:0.000000 .:@0.337158:0.573630:0.359901:0.573630:0.359901:0.557917:0.337158:0.557917:0.000000:0.000000:0.000000 x :@0.341109:0.573630:0.351804:0.573630:0.351804:0.558195:0.341109:0.558195:0.000000:0.000000 6:@0.351964:0.577530:0.356051:0.577530:0.356051:0.554248:0.351964:0.554248:0.000000 4. Obtén la hipérbola que pasa por los puntos ( 2 5, 3), 4, :@0.073089:0.609339:0.566595:0.609339:0.566595:0.592670:0.073089:0.592670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.465251:0.608785:0.480584:0.608785:0.480584:0.595069:0.465251:0.595069:0.000000 1:@0.540761:0.613473:0.544847:0.613473:0.544847:0.590191:0.540761:0.590191:0.000000 3:@0.592622:0.603469:0.601605:0.603469:0.601605:0.587757:0.592622:0.587757:0.000000 3:@0.570248:0.603622:0.579230:0.603622:0.579230:0.587909:0.570248:0.587909:0.000000 2:@0.583317:0.619446:0.592299:0.619446:0.592299:0.603733:0.583317:0.603733:0.000000 2:@0.606727:0.614517:0.610814:0.614517:0.610814:0.591235:0.606727:0.591235:0.000000 y tiene como eje principal el eje x. Para el :@0.611450:0.609339:0.930928:0.609339:0.930928:0.592670:0.611450:0.592670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 efecto, considera:@0.103209:0.625981:0.231884:0.625981:0.231884:0.609312:0.103209:0.609312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , ) :@0.113050:0.653609:0.228694:0.653609:0.228694:0.637897:0.113050:0.637897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.117000:0.653055:0.132334:0.653055:0.132334:0.639339:0.117000:0.639339:0.000000 x y:@0.140985:0.653609:0.162908:0.653609:0.162908:0.638174:0.140985:0.638174:0.000000:0.000000:0.000000 [:@0.171607:0.653319:0.186243:0.653319:0.186243:0.639909:0.171607:0.639909:0.000000 x:@0.236101:0.645199:0.243556:0.645199:0.243556:0.629764:0.236101:0.629764:0.000000 a:@0.235143:0.659899:0.244402:0.659899:0.244402:0.644464:0.235143:0.644464:0.000000 1 2:@0.228681:0.659084:0.251051:0.659084:0.251051:0.631232:0.228681:0.631232:0.000000:0.000000:0.000000 :@0.251066:0.647364:0.256809:0.647364:0.256809:0.630222:0.251066:0.630222:0.000000 :@0.257142:0.653609:0.280365:0.653609:0.280365:0.637897:0.257142:0.637897:0.000000:0.000000:0.000000 2:@0.261093:0.653055:0.276426:0.653055:0.276426:0.639339:0.261093:0.639339:0.000000 y:@0.287771:0.643861:0.295245:0.643861:0.295245:0.628426:0.287771:0.628426:0.000000 b:@0.286870:0.661848:0.296128:0.661848:0.296128:0.646413:0.286870:0.646413:0.000000 1 2:@0.280352:0.659463:0.302722:0.659463:0.302722:0.631612:0.280352:0.631612:0.000000:0.000000:0.000000 :@0.302737:0.647742:0.308480:0.647742:0.308480:0.630601:0.302737:0.630601:0.000000 1.:@0.308799:0.653609:0.339367:0.653609:0.339367:0.637897:0.308799:0.637897:0.000000:0.000000:0.000000:0.000000 5:@0.312014:0.653055:0.327347:0.653055:0.327347:0.639339:0.312014:0.639339:0.000000 Comprueba:@0.104638:0.684549:0.195179:0.684549:0.195179:0.667880:0.104638:0.667880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que: :@0.195073:0.684549:0.234722:0.684549:0.234722:0.668837:0.195073:0.668837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , ) | :@0.119498:0.711897:0.263256:0.711897:0.263256:0.696185:0.119498:0.696185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.123448:0.711343:0.138781:0.711343:0.138781:0.697627:0.123448:0.697627:0.000000 5:@0.142861:0.714725:0.146948:0.714725:0.146948:0.691443:0.142861:0.691443:0.000000 5:@0.159946:0.711343:0.175280:0.711343:0.175280:0.697627:0.159946:0.697627:0.000000 x y:@0.183931:0.711897:0.205854:0.711897:0.205854:0.696462:0.183931:0.696462:0.000000:0.000000:0.000000 [:@0.214552:0.711607:0.229189:0.711607:0.229189:0.698197:0.214552:0.698197:0.000000 R:@0.233058:0.711037:0.246348:0.711037:0.246348:0.698140:0.233058:0.698140:0.000000 2:@0.246250:0.705833:0.251487:0.705833:0.251487:0.696673:0.246250:0.696673:0.000000 x:@0.270649:0.702047:0.278104:0.702047:0.278104:0.686612:0.270649:0.686612:0.000000 4:@0.269747:0.720034:0.278730:0.720034:0.278730:0.703600:0.269747:0.703600:0.000000 1 2:@0.263230:0.717649:0.285599:0.717649:0.285599:0.689798:0.263230:0.689798:0.000000:0.000000:0.000000 :@0.285613:0.705613:0.290877:0.705613:0.290877:0.689179:0.285613:0.689179:0.000000 :@0.291691:0.711897:0.314914:0.711897:0.314914:0.696185:0.291691:0.696185:0.000000:0.000000:0.000000 2:@0.295641:0.711343:0.310975:0.711343:0.310975:0.697627:0.295641:0.697627:0.000000 y:@0.326745:0.702859:0.334218:0.702859:0.334218:0.687424:0.326745:0.687424:0.000000 5:@0.325843:0.720846:0.334825:0.720846:0.334825:0.705133:0.325843:0.705133:0.000000 1 2:@0.314770:0.718461:0.341698:0.718461:0.341698:0.690610:0.314770:0.690610:0.000000:0.000000:0.000000 :@0.341708:0.706424:0.346973:0.706424:0.346973:0.690712:0.341708:0.690712:0.000000 1 .:@0.347772:0.711897:0.383640:0.711897:0.383640:0.696185:0.347772:0.696185:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.351355:0.711343:0.366688:0.711343:0.366688:0.697627:0.351355:0.697627:0.000000 6:@0.375718:0.717239:0.379804:0.717239:0.379804:0.693957:0.375718:0.693957:0.000000 Obtén:@0.104633:0.742833:0.152911:0.742833:0.152911:0.726164:0.104633:0.726164:0.000000:0.000000:0.000000:0.000000:0.000000 los focos, la excentricidad, las rectas asíntotas, y :@0.152823:0.742833:0.501244:0.742833:0.501244:0.727121:0.152823:0.727121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 representa:@0.500849:0.742833:0.582380:0.742833:0.582380:0.726164:0.500849:0.726164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en tu cuaderno gráficamente esta hipérbola.:@0.582282:0.742833:0.908926:0.742833:0.908926:0.727121:0.582282:0.727121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5. Sigue paso a paso la solución del ejercicio y, al final, traza en tu cuaderno las gráficas de la hipérbola y de la :@0.073089:0.791639:0.930237:0.791639:0.930237:0.774970:0.073089:0.774970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 recta tangente .:@0.103214:0.808281:0.230850:0.808281:0.230850:0.791612:0.103214:0.791612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 T:@0.218388:0.808281:0.227113:0.808281:0.227113:0.791598:0.218388:0.791598:0.000000 Considera:@0.104631:0.839221:0.180830:0.839221:0.180830:0.822552:0.104631:0.822552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la hipérbola siguiente::@0.180727:0.839221:0.344815:0.839221:0.344815:0.823509:0.180727:0.823509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( , 3, 4) ( , ) | :@0.119498:0.872791:0.284602:0.872791:0.284602:0.857078:0.119498:0.857078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.172402:0.872236:0.187735:0.872236:0.187735:0.858521:0.172402:0.858521:0.000000 5:@0.191814:0.876733:0.195901:0.876733:0.195901:0.853451:0.191814:0.853451:0.000000 x y:@0.205280:0.872791:0.227203:0.872791:0.227203:0.857356:0.205280:0.857356:0.000000:0.000000:0.000000 [:@0.235896:0.872501:0.250533:0.872501:0.250533:0.859091:0.235896:0.859091:0.000000 R:@0.254402:0.871931:0.267693:0.871931:0.267693:0.859034:0.254402:0.859034:0.000000 2:@0.267594:0.866727:0.272831:0.866727:0.272831:0.857567:0.267594:0.857567:0.000000 x:@0.291993:0.866293:0.299448:0.866293:0.299448:0.850858:0.291993:0.850858:0.000000 3:@0.291036:0.881304:0.300836:0.881304:0.300836:0.864163:0.291036:0.864163:0.000000 1 2:@0.284574:0.880179:0.306943:0.880179:0.306943:0.852328:0.284574:0.852328:0.000000:0.000000:0.000000 :@0.306959:0.868458:0.312702:0.868458:0.312702:0.851317:0.306959:0.851317:0.000000 :@0.313035:0.872791:0.336258:0.872791:0.336258:0.857078:0.313035:0.857078:0.000000:0.000000:0.000000 2:@0.316985:0.872236:0.332319:0.872236:0.332319:0.858521:0.316985:0.858521:0.000000 y:@0.343664:0.863866:0.351138:0.863866:0.351138:0.848431:0.343664:0.848431:0.000000 4:@0.342762:0.882166:0.352562:0.882166:0.352562:0.864238:0.342762:0.864238:0.000000 1 2:@0.336244:0.879470:0.358614:0.879470:0.358614:0.851618:0.336244:0.851618:0.000000:0.000000:0.000000 :@0.358629:0.867748:0.364372:0.867748:0.364372:0.849820:0.358629:0.849820:0.000000 1 .:@0.364692:0.872791:0.400559:0.872791:0.400559:0.857078:0.364692:0.857078:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.368275:0.872236:0.383608:0.872236:0.383608:0.858521:0.368275:0.858521:0.000000 6:@0.392638:0.876974:0.396724:0.876974:0.396724:0.853692:0.392638:0.853692:0.000000 Halla:@0.104633:0.907038:0.142772:0.907038:0.142772:0.890369:0.104633:0.890369:0.000000:0.000000:0.000000:0.000000:0.000000 la recta tangente a la hipérbola en el punto 5, :@0.142680:0.907038:0.488344:0.907038:0.488344:0.891325:0.142680:0.891325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.463598:0.908706:0.467684:0.908706:0.467684:0.885425:0.463598:0.885425:0.000000 16:@0.488071:0.902124:0.506036:0.902124:0.506036:0.886412:0.488071:0.886412:0.000000:0.000000 3:@0.492875:0.915965:0.501858:0.915965:0.501858:0.900252:0.492875:0.900252:0.000000 2:@0.506413:0.911531:0.510499:0.911531:0.510499:0.888249:0.506413:0.888249:0.000000 .:@0.511132:0.907038:0.514335:0.907038:0.514335:0.891325:0.511132:0.891325:0.000000 De la definición ( , 3, 4), se tiene 3, 4. :@0.104633:0.937975:0.453696:0.937975:0.453696:0.922262:0.104633:0.922262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.352880:0.937975:0.362138:0.937975:0.362138:0.922540:0.352880:0.922540:0.000000 5:@0.366022:0.937420:0.381356:0.937420:0.381356:0.923705:0.366022:0.923705:0.000000 b:@0.401180:0.937975:0.410439:0.937975:0.410439:0.922540:0.401180:0.922540:0.000000 5:@0.414323:0.937420:0.429656:0.937420:0.429656:0.923705:0.414323:0.923705:0.000000 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