{"id":2391,"date":"2024-08-08T03:00:51","date_gmt":"2024-08-08T03:00:51","guid":{"rendered":"http:\/\/lash.utrng.edu.mx\/?p=2391"},"modified":"2024-08-09T05:26:39","modified_gmt":"2024-08-09T05:26:39","slug":"02-conicas-2da-parte","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=2391","title":{"rendered":"02 C\u00f3nicas 2da parte"},"content":{"rendered":"\n<p class=\"has-text-color has-background has-medium-font-size has-vivid-red-color has-pale-cyan-blue-background-color\"><strong>Ecuaciones de la Elipse<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-28.png\"><img loading=\"lazy\" decoding=\"async\" width=\"577\" height=\"312\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-28.png\" alt=\"\" class=\"wp-image-2392\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-28.png 577w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-28-300x162.png 300w\" sizes=\"auto, (max-width: 577px) 100vw, 577px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>Dados dos puntos fijos <strong>F<sub>1<\/sub> y F<sub>2<\/sub><\/strong> distintos, denominados Focos, se define la Elipse como el <strong>lugar geom\u00e9trico<\/strong> del conjunto de puntos <strong>P(x;y)<\/strong> tales que la suma de distancias de<strong> P<\/strong> a los focos  <strong>F<sub>1<\/sub> y F<sub>2<\/sub><\/strong>, es igual a una constante convencional <strong>2a<\/strong><\/p>\n\n\n\n<!--more-->\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-29.png\"><img loading=\"lazy\" decoding=\"async\" width=\"578\" height=\"467\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-29.png\" alt=\"\" class=\"wp-image-2393\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-29.png 578w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-29-300x242.png 300w\" sizes=\"auto, (max-width: 578px) 100vw, 578px\" \/><\/a><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"blob:http:\/\/lash.utrng.edu.mx\/9665954d-9e0d-4107-8e1d-62a40b6bd21e\"><img loading=\"lazy\" decoding=\"async\" width=\"511\" height=\"454\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-30.png\" alt=\"\" class=\"wp-image-2397\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-30.png 511w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-30-300x267.png 300w\" sizes=\"auto, (max-width: 511px) 100vw, 511px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>Toda Elipse es sim\u00e9trica con respecto a sus ejes de simetr\u00eda, es decir, con respecto al eje mayor y menor.<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"blob:http:\/\/lash.utrng.edu.mx\/2089189e-d0c9-4f37-865c-49949737053c\"><img loading=\"lazy\" decoding=\"async\" width=\"573\" height=\"320\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-31.png\" alt=\"\" class=\"wp-image-2398\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-31.png 573w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-31-300x168.png 300w\" sizes=\"auto, (max-width: 573px) 100vw, 573px\" \/><\/a><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"blob:http:\/\/lash.utrng.edu.mx\/179185a3-bff8-403b-a606-a5bc13a421c3\"><img loading=\"lazy\" decoding=\"async\" width=\"574\" height=\"677\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-32.png\" alt=\"\" class=\"wp-image-2399\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-32.png 574w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-32-254x300.png 254w\" sizes=\"auto, (max-width: 574px) 100vw, 574px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>A medida que los focos se acercan y la \u00abe\u00bb tiende a 0, la elipse se asemeja mas a una circunferencia:<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-33.png\"><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"307\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-33.png\" alt=\"\" class=\"wp-image-2400\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-33.png 418w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-33-300x220.png 300w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>A medida que los focos se alejan y la \u00abe\u00bb tiende a 1, la elipse se asemeja cada vez m\u00e1s a una linea recta<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"blob:http:\/\/lash.utrng.edu.mx\/93b2225a-87af-4688-a20a-4f8625c5ae78\"><img loading=\"lazy\" decoding=\"async\" width=\"509\" height=\"275\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-34.png\" alt=\"\" class=\"wp-image-2401\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-34.png 509w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-34-300x162.png 300w\" sizes=\"auto, (max-width: 509px) 100vw, 509px\" \/><\/a><\/figure><\/div>\n\n\n\n<p class=\"has-text-color has-vivid-cyan-blue-color\"><strong>Primera forma(Can\u00f3nica)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-35.png\"><img loading=\"lazy\" decoding=\"async\" width=\"276\" height=\"129\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-35.png\" alt=\"\" class=\"wp-image-2402\"\/><\/a><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"blob:http:\/\/lash.utrng.edu.mx\/389d6ad1-6a9f-487e-8788-cbca17bf3385\"><img loading=\"lazy\" decoding=\"async\" width=\"566\" height=\"435\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-36.png\" alt=\"\" class=\"wp-image-2403\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-36.png 566w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-36-300x231.png 300w\" sizes=\"auto, (max-width: 566px) 100vw, 566px\" \/><\/a><\/figure><\/div>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-vivid-cyan-blue-color\"><strong>Segunda Forma(Can\u00f3nica)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-37.png\"><img loading=\"lazy\" decoding=\"async\" width=\"481\" height=\"492\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-37.png\" alt=\"\" class=\"wp-image-2405\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-37.png 481w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-37-293x300.png 293w\" sizes=\"auto, (max-width: 481px) 100vw, 481px\" \/><\/a><figcaption>Cuando la elipse tiene su centro en el Origen y el eje Mayor esta sobre el eje Y<\/figcaption><\/figure><\/div>\n\n\n\n<p>Ecuaci\u00f3n de una elipse vertical can\u00f3nica:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-38.png\"><img loading=\"lazy\" decoding=\"async\" width=\"349\" height=\"212\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-38.png\" alt=\"\" class=\"wp-image-2408\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-38.png 349w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-38-300x182.png 300w\" sizes=\"auto, (max-width: 349px) 100vw, 349px\" \/><\/a><\/figure>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-vivid-cyan-blue-color\"><strong>Tercera Forma(Ordinaria)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-39.png\"><img loading=\"lazy\" decoding=\"async\" width=\"542\" height=\"291\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-39.png\" alt=\"\" class=\"wp-image-2409\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-39.png 542w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-39-300x161.png 300w\" sizes=\"auto, (max-width: 542px) 100vw, 542px\" \/><\/a><figcaption>Cuando la elipse tiene su centro en el punto C(h;k) y el eje Mayor es paralelo al eje X<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-40.png\"><img loading=\"lazy\" decoding=\"async\" width=\"342\" height=\"354\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-40.png\" alt=\"\" class=\"wp-image-2410\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-40.png 342w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-40-290x300.png 290w\" sizes=\"auto, (max-width: 342px) 100vw, 342px\" \/><\/a><\/figure><\/div>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-vivid-cyan-blue-color\"><strong>Cuarta Forma(Ordinaria)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-41.png\"><img loading=\"lazy\" decoding=\"async\" width=\"510\" height=\"440\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-41.png\" alt=\"\" class=\"wp-image-2412\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-41.png 510w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-41-300x259.png 300w\" sizes=\"auto, (max-width: 510px) 100vw, 510px\" \/><\/a><figcaption>Cuando la Elipse tiene su centro en el punto C(h;k) y el eje Mayor es paralelo al eje Y<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large is-resized\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-42.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-42.png\" alt=\"\" class=\"wp-image-2414\" width=\"274\" height=\"68\"\/><\/a><\/figure><\/div>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"347\" height=\"187\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-43.png\" alt=\"\" class=\"wp-image-2415\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-43.png 347w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-43-300x162.png 300w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/figure>\n\n\n\n<p class=\"has-text-color has-background has-medium-font-size has-vivid-red-color has-pale-cyan-blue-background-color\"><strong>Ejemplo 1<\/strong><\/p>\n\n\n\n<p>Demostrar que la ecuaci\u00f3n de una Elipse horizontal can\u00f3nica es:<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large is-resized\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-44.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-44.png\" alt=\"\" class=\"wp-image-2416\" width=\"166\" height=\"84\"\/><\/a><\/figure><\/div>\n\n\n\n<p>Sobre la elipse, tomaremos un punto gen\u00e9rico M(x;y) y luego aplicaremos la definici\u00f3n de la elipse.<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-45.png\"><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"225\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-45.png\" alt=\"\" class=\"wp-image-2417\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-45.png 418w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-45-300x161.png 300w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><\/a><\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Ecuaciones de la Elipse Dados dos puntos fijos F1 y F2 distintos, denominados Focos, se define la Elipse como el lugar geom\u00e9trico del conjunto de puntos P(x;y) tales que la suma de distancias de P a los focos F1 y F2, es igual a una constante convencional 2a<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[54],"tags":[],"class_list":["post-2391","post","type-post","status-publish","format-standard","hentry","category-tercerparcialfuncionesmate"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2391","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2391"}],"version-history":[{"count":6,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2391\/revisions"}],"predecessor-version":[{"id":3549,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2391\/revisions\/3549"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2391"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}