LA ELIPSE

[color=#0000ff]DEFINICIÓN[/color][br]La ELIPSE es el lugar geométrico de todos los puntos del plano cuya suma de distancias a dos puntos fijos llamados FOCOS es siempre constante.[br]           [img]data:image/png;base64,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[/img][br]
[color=#0000ff]ELEMENTOS DE LA ELIPSE[/color][br][img]https://www.geogebra.org/resource/hpecjcsh/lgarzedgWxmbTe1i/material-hpecjcsh.png[/img][list][*][b]Focos:[/b]  Son los puntos fijos F[/*][/list][justify][/justify][list][*] y F'.[br][/*][*][b]Eje focal o eje de simetría: [/b]Es la recta que pasa por los focos .[br][/*][*][b]Eje normal o eje secundario: [/b]es la recta perpendicular al eje focal, y pasa por el centro, es decir, es la mediatriz del segmento [img width=24,height=16]https://lh3.googleusercontent.com/60kkLeMtcmgd6T5H41VeJCqcTzrlTa0GbQJV7kuYXhAtyjmvmyyacwdF7dbVNQdVAhP1DEEsNYuLFZdSvQxxbC30SJidQiorOXKySDcUfMUNvelHrBLCdH5b_5Lf68EDnGcTTL3v[/img]. [br][/*][*][b]Centro C: [/b]punto medio del segmento que une los focos.[br][/*][*][b]Vértices primarios: [/b]Son los puntos V y V' en que el eje focal corta a la elipse.[br][/*][*][b]Vértices secundarios:[/b] Son los puntos B y B' en que el eje normal corta a la elipse.[br][/*][*][b]Eje focal: [/b]Es el segmento de longitud [img width=56,height=16]https://lh6.googleusercontent.com/d9GYDuxuLWC83R413MTfVpQmuOXhi50VEF-Xzi0ReeRO2TR2aKUvNm8GnKQ58zeMOwQxSnISaO14417SHma2qy4eeuY7HtgIyM31ONyEijHObdjjW3b9izxISf8YxDmA-WGbK-jN[/img], entonces, la semieje focal es [img width=84,height=16]https://lh3.googleusercontent.com/q2ucCENz5RqfOvwU6z0OO2OSeHWqj74UG13m52hJulgLXfMBUIwfqXhKoBgl53uonxMNh7S6jKDazrkOcMJdRMs73X_n1MN4AIYhL3S87g0vDKOGNrm2fXX_-_JcI_noWavGsoyq[/img].[br][/*][*][b]Eje mayor:[/b] Es el segmento de longitud [img width=56,height=16]https://lh3.googleusercontent.com/pMf6wQkqtjRq5wSi9-Qxi-vsOAv9wJaIUhrnKOdCkVBV5_86y7DvugP7-WNocw5SEjDsfMTw5FeYJmZO8zWahcqY3IBW0uABGYD1HDY_C1zKYz3wWEum3bO9JJl-zaDjX5qyL1zn[/img], entonces, el semieje mayor es [img width=85,height=16]https://lh3.googleusercontent.com/Yg5Bq6OT9SiCoLqqdaFvv6ejl4wzwJCDKwkwxmm2Ftn9Ooa_VPfhiaL6tirO82ZJXHMF8pvNkPf2CAUxnLl54ucrLhIbBDwXH4HBauwNpDggqLpVAGbENbnrfTr97FeFAK84Z1Ip[/img].[br][/*][*][b]Eje menor: [/b]Es el segmento de longitud [img width=56,height=16]https://lh4.googleusercontent.com/uQXMwKY-RsxasIqpX1ZSynGNrYZAQ8oBJ_4ovzvG2t4gbSlf9khy8WoDFU8eoXnHq2qVV1vtGwVRUJPenGOHFchXL7yG-DYwR9eQylonzrxmFVqAY6HZggD_Ixn9nONHjXS-S8JQ[/img], entonces, el semieje menor es [img width=85,height=16]https://lh6.googleusercontent.com/6aJBaiTD-HihzrLF2HcKHWNejY9axThnYIMpIuYHvmiyfAnbl3IEhYubzdAD74ZfBRRYP9GEOMXepiK12QN6ObscxS8kDWTEDZPVsPRwlBheLNv-q3NeoyNe97mWi65hcFCQjoxO[/img].[br][/*][*][b]Excentricidad e:[/b] Es una cantidad constante para cada elipse, es un número que mide el mayor o menor achatamiento de la elipse. Se calcula dividiendo la longitud del semieje focal entre la longitud del semieje mayor, de la siguiente manera:[br][/*][/list][img width=235,height=29]https://lh4.googleusercontent.com/ukmohKBumqCJBhkOcS_K5jUaeuvCCpb7-siba80McJ42r_Z5KocrQxwAxL0kuN3vewoZXmn_PVJwrH2k7Y5Ym9zjHj2N7hSCccyDzyYiETIeimXjk9BNfkFrrR46UfXj89rI3X8_[/img][br][list][*][b]Lado Recto (LR): [/b]Segmento de recta perpendicular al eje mayor, contiene a un foco (cualquiera de los dos) y sus extremos se localizan sobre la elipse. La longitud del lado recto se denomina ancho focal, y se calcula mediante:[br][/*][/list]                                     [img width=67,height=36]https://lh3.googleusercontent.com/oDUUORxiQN_L11K5LQgV_dHkK5EA2QaCM6LEuFkjrOaGcPVcSYjjecfsceZD6CnvJpEJT5J32RzCQsB3-E1pE3LAZnsjTO3PE1wZWRKdmUmsM9ODR6XeVNl-9iwxlndZT3Ss52ju[/img][br][list][*][b]Rectas Directrices: [/b]Cada foco F de la elipse está asociado con una recta paralela al eje menor llamada [url=https://es.wikibooks.org/w/index.php?title=Directriz&action=edit&redlink=1]directriz[/url]. La distancia de cualquier punto P de la elipse hasta el foco F es una fracción constante de la distancia perpendicular de ese punto P a la directriz.[br][/*][*][b]Radios focales:[/b] Son los segmentos [img width=20,height=15]https://lh6.googleusercontent.com/l2Pq4BoP1PatlDLh27w7EfyNWjLBWb-Y0E3uNB31qbghz_EbqjTpMPM6BWuC2yuje1b-05TGJWnuydBrb7aHTpkkSNvKVBm_Stf4kAM30k69ue_1_NxD_XgKTVp_igf8QtcXX5oD[/img] y [img width=24,height=16]https://lh4.googleusercontent.com/pk-k9pLpqEMX8L6wDSMAuv03MEhFnxrhWafc4wJFcxGgfxPUgOqvUFhlOyV_VyWRMQWtUHfcSNI_HlYEaU3OwWOe2DguXLT1ebNAxMkdXaQ1PjF5kR8WEPERGhczn9d2GXdCFb-g[/img], determinados por un punto de la curva y los focos.[br][/*][*][b]Definición de la elipse: [/b][img width=93,height=16]https://lh6.googleusercontent.com/toTQZpK9kDwotdZqs66d6i9jykxNE_coRX27MrzYrE2hWAiRmuPLKk6tl3OwvHNf09TMmXsf9w-YZlVRvMhtZF2RN1d2JWpUN-zbtG0L4UIog2g64_V0sloJC3zFMIuYwQAhtPEj[/img] ([img width=16,height=9]https://lh6.googleusercontent.com/9C8wblA8tZWY9qNhtP0l86kM4wBpEzEzdQmeCLlvZddKkqQCmt-Rn6XkhmP_ykWYcmUjhIaGAlKoSCVHGa0Rem29UAfBhCILHb_nQdtAvNeZ9dGor7Cyk6czPlLFaInGRMbEozG7[/img]= constante)[/*][*][b]Relación fundamental de la elipse: [/b][img width=79,height=12]https://lh5.googleusercontent.com/_W6huaTUAJooHcssVi61wrU9u28qJmx2pM-VNvGKqb1fe-La0sMNLCDbSyRzMLpAEw4hz__ofyFnATWzgIb8AkbtEoct0F44yR6Y-jXMoOb-NNVFkAiV1rrStykoMSlXDTp4fqXa[/img][/*][/list]
[color=#0000ff][justify][b]Si el centro está en el origen (0,0) estas ecuaciones se reducen a:[br][/b][/justify][list][*][b]centro en el origen (0,0) y eje focal paralelo al eje x[/b][/*][/list][b][br][/b]      [img width=88,height=39]https://lh5.googleusercontent.com/o879KGNKklt2Ayl9mxmqJ0Yp__4XAsq53AQOP-AKZFBLPoaP3XuFvcuA4lwL1UOnmN23FIPqh6IYHeHqTldfkrxEk_n7SUvFS4JbYNJStZxesjEun75DOnwBm-yaiAfM0FK6z77d[/img][br][/color][br]Eje paralelo al eje x o eje horizontal:[br][list][*]El centro se encuentra en el origen: [img width=53,height=12]https://lh5.googleusercontent.com/WR5dzYpkHRvjdp435ENjkkl7zDxQh9yInD2CWHPXtgqlu1rOfgBo4ry3-SLyqfeZ_M_T4cfua5ORiRO520POUbMTx4Auj51u_dJsPKsGc-U2M4KBjPAxSpAyM3l8o_Pad1hTSPYD[/img][br][/*][/list][br][img]data:image/png;base64,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