{"id":236,"date":"2023-07-10T18:00:41","date_gmt":"2023-07-10T18:00:41","guid":{"rendered":"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/"},"modified":"2023-07-10T18:00:41","modified_gmt":"2023-07-10T18:00:41","slug":"excentricidade-da-elipse","status":"publish","type":"post","link":"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/","title":{"rendered":"Calcule a excentricidade da elipse"},"content":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 o significado da excentricidade da elipse e como ela \u00e9 calculada (f\u00f3rmula). Al\u00e9m disso, voc\u00ea ver\u00e1 exemplos de c\u00e1lculos de excentricidade de elipse. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-excentricidad-de-la-elipse\"><\/span> Qual \u00e9 a excentricidade da elipse?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A excentricidade da elipse \u00e9 um par\u00e2metro que mede o qu\u00e3o redonda ou achatada \u00e9 uma elipse, ou seja, a excentricidade de uma elipse indica o quanto a elipse se assemelha a um c\u00edrculo.<\/strong> <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> Por outro lado, lembremos tamb\u00e9m em que consiste uma elipse: a elipse \u00e9 o <a href=\"https:\/\/mathority.org\/pt\/definicao-e-exemplos-de-locus\/\">lugar geom\u00e9trico<\/a> de todos os pontos de um plano cuja soma das dist\u00e2ncias a dois outros pontos fixos (chamados focos F e F&#8217;) \u00e9 constante. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-excentricidad-de-la-elipse\"><\/span> F\u00f3rmula de excentricidade da elipse <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p> Depois de vermos a defini\u00e7\u00e3o da excentricidade da elipse, vamos ver como ela \u00e9 calculada a partir de sua f\u00f3rmula: <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> A <strong>f\u00f3rmula para a excentricidade da elipse<\/strong> \u00e9 a seguinte:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7290cf41b85af2331d8634e251ca44b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e=\\cfrac{c}{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"44\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"text-align:left; margin-bottom:4px\"> Ouro:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3fc193f43cc29c1eef788f64ba43c1bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a excentricidade da elipse<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-41a04eeea923a1a0c28094a8a4680525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a dist\u00e2ncia de um foco (pontos F e F&#8217;) da elipse ao seu centro<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o comprimento do semieixo maior (ou maior) da elipse. <\/li>\n<\/ul>\n<\/div>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-dexcentricite-de-lellipse.webp\" alt=\"f\u00f3rmula para a excentricidade de uma elipse\" class=\"wp-image-2143\" width=\"343\" height=\"339\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Lembre-se de que os focos de uma elipse s\u00e3o os pontos fixos cuja soma das dist\u00e2ncias a qualquer ponto da elipse \u00e9 constante. Al\u00e9m disso, a dist\u00e2ncia entre os dois pontos focais \u00e9 chamada de dist\u00e2ncia focal.<\/p>\n<p> O valor da excentricidade varia de zero, o que significa que \u00e9 um c\u00edrculo perfeito, a um, o que significa que \u00e9 uma linha horizontal. Obviamente 0 e 1 n\u00e3o est\u00e3o inclu\u00eddos porque os objetos geom\u00e9tricos resultantes n\u00e3o s\u00e3o mais elipses.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14599d3dfc5dd832ced7cdb4378e4065_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0 Par cons\u00e9quent, comme vous pouvez le voir dans la repr\u00e9sentation graphique ci-dessous, plus la valeur de l'excentricit\u00e9 de l'ellipse est petite, plus elle ressemble \u00e0 un cercle, au contraire, plus le coefficient est grand, plus l'ellipse est aplatie. \n\n<div class=&quot;wp-block-image&quot;>\n<figure class=&quot;aligncenter size-large is-resized&quot;><img decoding=&quot;async&quot; loading=&quot;lazy&quot; src=&quot;https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/excentricite-dellipse.webp&quot; alt=&quot;valeur de l'excentricit\u00e9 de l'ellipse&quot; class=&quot;wp-image-2095&quot; width=&quot;669&quot; height=&quot;154&quot; srcset=&quot;&quot; sizes=&quot;&quot;><\/figure>\n<\/div>\n<p> En bref, l&#8217;excentricit\u00e9 d&#8217;une ellipse est un coefficient dont la valeur d\u00e9termine la forme qu&#8217;elle a. <\/p>\n<div class=&quot;adsb30&quot; style=&quot; margin:12px; text-align:center&quot;>\n<div id=&quot;ezoic-pub-ad-placeholder-109&quot;><\/div>\n<\/div>\n<p> Si vous \u00eates plus int\u00e9ress\u00e9 par les caract\u00e9ristiques d&#8217;une ellipse, vous pouvez vous r\u00e9f\u00e9rer \u00e0 l&#8217; <a href=&quot;https:\/\/mathority.org\/equation-de-la-formule-de-l'ellipse\/&quot;>\u00e9quation de l&#8217;ellipse<\/a> . Sur cette page, vous trouverez une explication d\u00e9taill\u00e9e de ce qu&#8217;est une ellipse, de tous ses \u00e9l\u00e9ments et de la fa\u00e7on dont son \u00e9quation est calcul\u00e9e. Et, en plus, vous pourrez voir plusieurs exemples, exercices et probl\u00e8mes r\u00e9solus sur des ellipses. <\/p>\n<h2 class=&quot;wp-block-heading&quot;><span class=&quot;ez-toc-section&quot; id=&quot;relacion-importante-para-hallar-la-excentricidad-de-la-elipse&quot;><\/span> Relation importante pour trouver l&#8217;excentricit\u00e9 de l&#8217;ellipse<span class=&quot;ez-toc-section-end&quot;><\/span><\/h2>\n<p> Les diff\u00e9rents \u00e9l\u00e9ments d&#8217;une ellipse sont li\u00e9s les uns aux autres. De plus, les relations entre eux sont tr\u00e8s importantes pour les exercices sur les ellipses, car elles sont g\u00e9n\u00e9ralement n\u00e9cessaires pour r\u00e9soudre des probl\u00e8mes sur les ellipses et d\u00e9terminer leurs \u00e9quations. Comme nous l&#8217;avons vu plus haut dans l&#8217;explication de la notion d&#8217;excentricit\u00e9 de l&#8217;ellipse, la distance de tout point de l&#8217;ellipse au foyer F plus la distance du m\u00eame point au foyer F&#8217; est constante. Eh bien, cette valeur constante est \u00e9gale \u00e0 deux fois ce que mesure le demi-grand axe. Autrement dit, l&#8217;\u00e9galit\u00e9 suivante vaut pour tout point d&#8217;une ellipse :&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;478&#8243; width=&#8221;3899&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<p> d(P,F) + d(P,F&#8217;)= 2a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c2b5745fffac46d01eb44166fb263ed6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" O\u00f9\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"24\" style=\"vertical-align: 0px;\"><\/p>\n<p> d(P,F)<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34cba514525aad2083c7dec3111c8d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"et\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> d(P,F&#8217;)<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-196b5f01a7de97251db68211ac7c5116_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"est la distance du point P au foyer F et F' respectivement et\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"424\" style=\"vertical-align: -4px;\"><\/p>\n<p> tem<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0a64e3f6d477fb8b92938774b2debd7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"est la longueur de l'axe semi-focal. Par cons\u00e9quent, puisque le sommet de l'axe secondaire est juste au milieu de l'axe principal, la distance de celui-ci \u00e0 l'un des foyers est \u00e9quivalente \u00e0 la longueur du demi-axe principal (\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"1088\" style=\"vertical-align: -5px;\"><\/p>\n<p> tem<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7fa84c41ca006919409ec34bb4eabaa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"): \n\n<div class=&quot;wp-block-image&quot;>\n<figure class=&quot;aligncenter size-large is-resized&quot;><img decoding=&quot;async&quot; loading=&quot;lazy&quot; src=&quot;https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/relation-delements-dellipse.webp&quot; alt=&quot;\u00e9quation de preuve d'ellipse&quot; class=&quot;wp-image-2087&quot; width=&quot;332&quot; height=&quot;197&quot; srcset=&quot;&quot; sizes=&quot;&quot;><\/figure>\n<\/div>\n<p> Par cons\u00e9quent, \u00e0 partir du th\u00e9or\u00e8me de Pythagore, il est possible de trouver <strong>la relation qui existe entre le demi-axe principal, le demi-axe secondaire et la distance semi-focale d&#8217;une ellipse :<\/strong>&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;195&#8243; width=&#8221;582&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<p> a^2=b^2+c^2<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d17620f5d1ac3496df21cdce30ad9fc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Retenez \u00e9galement cette autre formule car elle vous sera tr\u00e8s utile pour calculer le r\u00e9sultat des exercices avec des ellipses. \n\n<h2 class=&quot;wp-block-heading&quot;><span class=&quot;ez-toc-section&quot; id=&quot;ejemplo-de-como-calcular-la-excentricidad-de-la-elipse&quot;><\/span> Exemple de calcul de l&#8217;excentricit\u00e9 de l&#8217;ellipse<span class=&quot;ez-toc-section-end&quot;><\/span><\/h2>\n<p> Vous trouverez ci-dessous un exercice r\u00e9solu pour voir comment l&#8217;excentricit\u00e9 d&#8217;une ellipse est calcul\u00e9e :<\/p>\n<ul>\n<li> Trouver l&#8217;excentricit\u00e9 de l&#8217;ellipse dont le demi-grand axe et le demi-grand axe mesurent respectivement 5 et 3 unit\u00e9s.<\/li>\n<\/ul>\n<p> Pour trouver la valeur de l&#8217;excentricit\u00e9 de l&#8217;ellipse, il faut conna\u00eetre la longueur du demi-axe principal et la longueur du segment entre un foyer et le centre de l&#8217;ellipse. Nous connaissons d\u00e9j\u00e0 le premier, nous n&#8217;avons donc qu&#8217;\u00e0 d\u00e9terminer la distance semi-focale. A partir de la formule de la relation entre les \u00e9l\u00e9ments d&#8217;une ellipse, on peut calculer combien vaut la demi-distance focale : &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;193&#8243; width=&#8221;2952&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<p> a^2=b^2+c^2 c^2=a^2-b^2 c=\\sqrt{a^2-b^2} = \\sqrt{5^2-3^2}=\\sqrt {16} = 4<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05a82fe932095d842744854d443304ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Et quand on conna\u00eet d\u00e9j\u00e0 la valeur des termes\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"328\" style=\"vertical-align: -4px;\"><\/p>\n<p> tem<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34cba514525aad2083c7dec3111c8d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"et\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> contra,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad162aa4c12617a7e88c19db14dc717f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Nous pouvons maintenant d\u00e9terminer l'excentricit\u00e9 de l'ellipse :\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"483\" style=\"vertical-align: -4px;\"><\/p>\n<p> e= \\cfrac{c}{a} = \\cfrac{4}{5} = \\bm{0,8} $<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nesta p\u00e1gina voc\u00ea encontrar\u00e1 o significado da excentricidade da elipse e como ela \u00e9 calculada (f\u00f3rmula). Al\u00e9m disso, voc\u00ea ver\u00e1 exemplos de c\u00e1lculos de excentricidade de elipse. Qual \u00e9 a excentricidade da elipse? A excentricidade da elipse \u00e9 um par\u00e2metro que mede o qu\u00e3o redonda ou achatada \u00e9 uma elipse, ou seja, a excentricidade de &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/\"> <span class=\"screen-reader-text\">Calcule a excentricidade da elipse<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[10],"tags":[],"class_list":["post-236","post","type-post","status-publish","format-standard","hentry","category-conico"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Calcular a excentricidade da elipse - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Calcular a excentricidade da elipse - Mathority\" \/>\n<meta property=\"og:description\" content=\"Nesta p\u00e1gina voc\u00ea encontrar\u00e1 o significado da excentricidade da elipse e como ela \u00e9 calculada (f\u00f3rmula). Al\u00e9m disso, voc\u00ea ver\u00e1 exemplos de c\u00e1lculos de excentricidade de elipse. Qual \u00e9 a excentricidade da elipse? A excentricidade da elipse \u00e9 um par\u00e2metro que mede o qu\u00e3o redonda ou achatada \u00e9 uma elipse, ou seja, a excentricidade de &hellip; Calcule a excentricidade da elipse Leia mais &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T18:00:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7290cf41b85af2331d8634e251ca44b9_l3.png\" \/>\n<meta name=\"author\" content=\"Equipe Mathoridade\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Equipe Mathoridade\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/\"},\"author\":{\"name\":\"Equipe Mathoridade\",\"@id\":\"https:\/\/mathority.org\/pt\/#\/schema\/person\/26defeb7b79f5baaedafa33a1ac6ac00\"},\"headline\":\"Calcule a excentricidade da elipse\",\"datePublished\":\"2023-07-10T18:00:41+00:00\",\"dateModified\":\"2023-07-10T18:00:41+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/\"},\"wordCount\":304,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/pt\/#organization\"},\"articleSection\":[\"C\u00f4nico\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/\",\"url\":\"https:\/\/mathority.org\/pt\/excentricidade-da-elipse\/\",\"name\":\"Calcular a excentricidade da elipse - 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