{"id":10050,"date":"2022-02-15T17:38:29","date_gmt":"2022-02-15T12:08:29","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10050"},"modified":"2022-02-16T22:10:12","modified_gmt":"2022-02-16T16:40:12","slug":"eccentricity-of-ellipse-formula-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/","title":{"rendered":"Eccentricity of Ellipse – Formula and Examples"},"content":{"rendered":"

Here you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples.<\/p>\n

Let’s begin –<\/p>\n

Eccentricity of Ellipse Formula<\/h2>\n

(i) For the ellipse \\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1, a > b<\/strong><\/h4>\n

we have,  \\(b^2\\) = \\(a^2(1 – e^2)\\)<\/p>\n

\\(\\implies\\)  \\(e^2\\) = 1 – \\(b^2\\over a^2\\)<\/p>\n

\\(\\implies\\)  eccentricity (e) = \\(\\sqrt{1 – {b^2\\over a^2}}\\)<\/p><\/blockquote>\n

(ii) For the ellipse \\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1, a < b<\/strong><\/h4>\n

eccentricity (e) = \\(\\sqrt{1 – {a^2\\over b^2}}\\)<\/p><\/blockquote>\n

Also Read<\/strong> : Different Types of Ellipse Equations and Graph<\/a><\/p>\n

Example<\/strong><\/span> : For the given ellipses, find the eccentricity.<\/p>\n

(i)  \\(16x^2 + 25y^2\\) = 400<\/p>\n

(ii)  \\(x^2 + 4y^2 – 2x\\) = 0<\/p>\n

Solution<\/strong><\/span> :<\/p>\n

(i)<\/strong>  We have,<\/p>\n

\\(16x^2 + 25y^2\\) = 400 \\(\\implies\\) \\(x^2\\over 25\\) + \\(y^2\\over 16\\),<\/p>\n

where \\(a^2\\) = 25 and \\(b^2\\) = 16 i.e. a = 5 and b = 4<\/p>\n

Clearly a > b,<\/p>\n

Therefore, the eccentricity of ellipse (e) = \\(\\sqrt{1 – {b^2\\over a^2}}\\)<\/p>\n

e = \\(\\sqrt{1 – 16\/25}\\) = \\(3\\over 5\\)<\/p>\n

(ii) <\/strong>We have,<\/p>\n

\\(x^2 + 4y^2 – 2x\\) = 0<\/p>\n

\\(\\implies\\) \\((x – 1)^2\\) + 4\\((y – 0)^2\\) = 1<\/p>\n

\\(\\implies\\)  \\((x – 1)^2\\over 1^2\\) + \\((y – 0)^2\\over (1\/2)^2\\) = 1<\/p>\n

Here, a = 1 and b = 1\/2<\/p>\n

Clearly a > b,<\/p>\n

Therefore, the eccentricity of ellipse (e) = \\(\\sqrt{1 – {b^2\\over a^2}}\\)<\/p>\n

e = \\(\\sqrt{1 – 1\/4}\\) = \\(\\sqrt{3}\\over 2\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples. Let’s begin – Eccentricity of Ellipse Formula (i) For the ellipse \\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1, a > b we have,  \\(b^2\\) = \\(a^2(1 – e^2)\\) \\(\\implies\\)  \\(e^2\\) = 1 – \\(b^2\\over a^2\\) \\(\\implies\\)  eccentricity …<\/p>\n

Eccentricity of Ellipse – Formula and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":""},"categories":[24],"tags":[],"yoast_head":"\nEccentricity of Ellipse - Formula and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Eccentricity of Ellipse - Formula and Examples\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-02-15T12:08:29+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-02-16T16:40:12+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Eccentricity of Ellipse – Formula and Examples\",\"datePublished\":\"2022-02-15T12:08:29+00:00\",\"dateModified\":\"2022-02-16T16:40:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/\"},\"wordCount\":199,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Ellipse\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/\",\"url\":\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/\",\"name\":\"Eccentricity of Ellipse - Formula and Examples\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2022-02-15T12:08:29+00:00\",\"dateModified\":\"2022-02-16T16:40:12+00:00\",\"description\":\"In this post you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Eccentricity of Ellipse – Formula and Examples\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Eccentricity of Ellipse - Formula and Examples","description":"In this post you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/","og_locale":"en_US","og_type":"article","og_title":"Eccentricity of Ellipse - Formula and Examples","og_description":"In this post you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples","og_url":"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/","og_site_name":"Mathemerize","article_published_time":"2022-02-15T12:08:29+00:00","article_modified_time":"2022-02-16T16:40:12+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Eccentricity of Ellipse – Formula and Examples","datePublished":"2022-02-15T12:08:29+00:00","dateModified":"2022-02-16T16:40:12+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/"},"wordCount":199,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Ellipse"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/","url":"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/","name":"Eccentricity of Ellipse - Formula and Examples","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2022-02-15T12:08:29+00:00","dateModified":"2022-02-16T16:40:12+00:00","description":"In this post you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples","breadcrumb":{"@id":"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/eccentricity-of-ellipse-formula-and-examples\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Eccentricity of Ellipse – Formula and Examples"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/10050"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=10050"}],"version-history":[{"count":7,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/10050\/revisions"}],"predecessor-version":[{"id":10141,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/10050\/revisions\/10141"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=10050"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=10050"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=10050"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}