{"id":2325,"date":"2024-08-08T04:00:00","date_gmt":"2024-08-08T04:00:00","guid":{"rendered":"http:\/\/lash.utrng.edu.mx\/?p=2325"},"modified":"2024-08-09T05:26:06","modified_gmt":"2024-08-09T05:26:06","slug":"01-conicas","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=2325","title":{"rendered":"01 C\u00f3nicas 1ra parte"},"content":{"rendered":"\n<p> Una Secci\u00f3n c\u00f3nica es la intersecci\u00f3n de un plano con un cono<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"540\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/conicas.1.png\" alt=\"\" class=\"wp-image-2326\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/conicas.1.png 960w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/conicas.1-300x169.png 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/conicas.1-768x432.png 768w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"439\" height=\"483\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-1.png\" alt=\"\" class=\"wp-image-2332\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-1.png 439w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-1-273x300.png 273w\" sizes=\"auto, (max-width: 439px) 100vw, 439px\" \/><\/figure><\/div>\n\n\n\n<!--more-->\n\n\n\n<p>La ecuaci\u00f3n general para cualquier secci\u00f3n c\u00f3nica es:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image.png\" alt=\"\" class=\"wp-image-2331\" width=\"489\" height=\"36\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image.png 489w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-300x22.png 300w\" sizes=\"auto, (max-width: 489px) 100vw, 489px\" \/><\/figure>\n\n\n\n<p>donde A, B, C, D, E y F, son Constantes<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Circunferencia<\/strong>:<ul><li>Si el plano es perpendicular a la Directriz, y no pasa por el v\u00e9rtice, entonces la intersecci\u00f3n del plano con el v\u00e9rtice es una Circunferencia.<\/li><\/ul><\/li><li><strong>Elipse<\/strong>:<ul><li>Si el plano cortante no es paralelo a una Generatriz ni a la Directriz, y no pasa por el v\u00e9rtice del cono, es una Elipse<\/li><\/ul><\/li><li><strong>Par\u00e1bola<\/strong>:<ul><li>Cuando el plano cortante es paralelo a una Generatriz y no pasa por el v\u00e9rtice, entonces se forma una Par\u00e1bola.<\/li><\/ul><\/li><li><strong>Hip\u00e9rbola<\/strong>:<ul><li>Si el plano cortante es paralelo a la Directriz del cono y no pasa por el v\u00e9rtice, se genera una Hip\u00e9rbola<\/li><\/ul><\/li><\/ul>\n\n\n\n<p class=\"has-text-color has-vivid-red-color\"><strong>Lugar Geom\u00e9trico<\/strong>:<\/p>\n\n\n\n<p>Conjunto de puntos que cumplen una misma propiedad. Por ejemplo:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>La Bisectriz de un \u00e1ngulo.<\/li><li>La mediatriz de un segmento.<\/li><li>La circunferencia<\/li><li>La superficie esf\u00e9rica, etc.<\/li><\/ul>\n\n\n\n<p><strong>Las c\u00f3nicas<\/strong>, son denominadas <strong>lugares geom\u00e9tricos<\/strong>, porque todos sus puntos cumplen la misma propiedad.<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"407\" height=\"300\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-2.png\" alt=\"\" class=\"wp-image-2336\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-2.png 407w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-2-300x221.png 300w\" sizes=\"auto, (max-width: 407px) 100vw, 407px\" \/><\/figure><\/div>\n\n\n\n<p>La constante<strong> e<\/strong> se denomina <strong>excentricidad <\/strong>del lugar geom\u00e9trico, y determina la forma y tipo de las curvas:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>si <strong>e=0<\/strong>, entonces la c\u00f3nica es una <strong>Circunferencia<\/strong><\/li><li>si <strong>e=1<\/strong>, entonces la c\u00f3nica es una <strong>Par\u00e1bola<\/strong><\/li><li>si <strong>e&lt;1<\/strong>, entonces la c\u00f3nica es una <strong>Elipse<\/strong><\/li><li> si<strong> e&gt;1<\/strong>, entonces la c\u00f3nica es una <strong>Hip\u00e9rbola<\/strong><\/li><\/ul>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-text-color has-background has-medium-font-size has-very-dark-gray-color has-luminous-vivid-amber-background-color\"><strong>Ecuaciones de la Circunferencia:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"355\" height=\"39\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-3.png\" alt=\"\" class=\"wp-image-2339\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-3.png 355w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-3-300x33.png 300w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-5.png\" alt=\"\" class=\"wp-image-2341\" width=\"406\" height=\"308\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-5.png 363w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-5-300x227.png 300w\" sizes=\"auto, (max-width: 406px) 100vw, 406px\" \/><\/figure><\/div>\n\n\n\n<p>Donde:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Centro:c(h;k)<\/li><li>Radio: R<\/li><li>Punto gen\u00e9rico:P(x;y)<\/li><\/ul>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-vivid-cyan-blue-color\"><strong>Ecuaci\u00f3n Ordinaria de la Circunferencia<\/strong>:<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-6.png\" alt=\"\" class=\"wp-image-2342\" width=\"216\" height=\"46\"\/><figcaption><strong>Ecuaci\u00f3n Can\u00f3nica<\/strong><\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-7.png\" alt=\"\" class=\"wp-image-2344\" width=\"356\" height=\"288\"\/><figcaption>Es cuando la circunferencia tiene su centro en el Origen de coordenadas<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-3.png\" alt=\"La imagen tiene un atributo ALT vac\u00edo; su nombre de archivo es image-3.png\"\/><figcaption><strong>Ecuaci\u00f3n Ordinaria<\/strong><\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-8.png\" alt=\"\" class=\"wp-image-2347\" width=\"396\" height=\"263\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-8.png 501w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-8-300x199.png 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-8-75x50.png 75w\" sizes=\"auto, (max-width: 396px) 100vw, 396px\" \/><figcaption>Es cuando la circunferencia tiene su centro en el Punto c(h;k)<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-vivid-cyan-blue-color\"><strong>Ecuaciones Particulares de la Circunferencia:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"366\" height=\"360\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-10.png\" alt=\"\" class=\"wp-image-2351\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-10.png 366w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-10-300x295.png 300w\" sizes=\"auto, (max-width: 366px) 100vw, 366px\" \/><figcaption>Circunferencia Tangente al eje X<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"347\" height=\"233\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-11.png\" alt=\"\" class=\"wp-image-2352\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-11.png 347w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-11-300x201.png 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-11-75x50.png 75w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><figcaption>Circunferencia Tangente al eje Y<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"366\" height=\"344\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-12.png\" alt=\"\" class=\"wp-image-2353\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-12.png 366w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-12-300x282.png 300w\" sizes=\"auto, (max-width: 366px) 100vw, 366px\" \/><figcaption>Circunferencias Tangentes a los ejes coordenados<\/figcaption><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\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:<\/strong><\/p>\n\n\n\n<p>En la siguiente figura hallar <strong>el Per\u00edmetro<\/strong> del rect\u00e1ngulo, se sabe que el \u00e1rea del rect\u00e1ngulo es de 100 cm<sup>2<\/sup> y que el radio de la circunferencia es 10<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"298\" height=\"284\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-13.png\" alt=\"\" class=\"wp-image-2354\"\/><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>Per\u00edmetro del Rect\u00e1ngulo = ?<\/li><li> Per\u00edmetro del Rect\u00e1ngulo = 2a + 2b = ?<\/li><li>Ecuaci\u00f3n de la Circunferencia:  x<sup>2<\/sup>  + y<sup>2<\/sup>  = 100 &#8212;->a<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"322\" height=\"297\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-15.png\" alt=\"\" class=\"wp-image-2356\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-15.png 322w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-15-300x277.png 300w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/figure><\/div>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"512\" height=\"135\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-16.png\" alt=\"\" class=\"wp-image-2357\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-16.png 512w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-16-300x79.png 300w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure>\n\n\n\n<p>por el dato de que el <strong>\u00e1rea del rect\u00e1ngulo=100<\/strong>, se tiene que<strong> ab=100<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"218\" height=\"69\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-17.png\" alt=\"\" class=\"wp-image-2358\"\/><\/figure><\/div>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"362\" height=\"402\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-18.png\" alt=\"\" class=\"wp-image-2360\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-18.png 362w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-18-270x300.png 270w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"542\" height=\"258\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-19.png\" alt=\"\" class=\"wp-image-2362\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-19.png 542w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/03\/image-19-300x143.png 300w\" sizes=\"auto, (max-width: 542px) 100vw, 542px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Una Secci\u00f3n c\u00f3nica es la intersecci\u00f3n de un plano con un cono<\/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":[52],"tags":[],"class_list":["post-2325","post","type-post","status-publish","format-standard","hentry","category-segundoparcialfuncionesmate"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2325","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=2325"}],"version-history":[{"count":13,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2325\/revisions"}],"predecessor-version":[{"id":3548,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2325\/revisions\/3548"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2325"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2325"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}