{"id":3934,"date":"2021-08-10T12:51:27","date_gmt":"2021-08-10T12:51:27","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3934"},"modified":"2022-02-16T21:50:28","modified_gmt":"2022-02-16T16:20:28","slug":"different-types-of-ellipse","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/different-types-of-ellipse\/","title":{"rendered":"Different Types of Ellipse Equations and Graph"},"content":{"rendered":"

Here, you will learn different types of ellipse and their basic definitions with their graphs.<\/p>\n

Let’s begin –<\/p>\n

Different Types of Ellipse<\/h2>\n

(a)\u00a0 First type of Ellipse<\/strong> is<\/p>\n

\n

\\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1, where a > b<\/p>\n<\/blockquote>\n

\"ellipse<\/p>\n

\u00a0<\/p>\n

(a)\u00a0 AA’ = Major axis = 2a<\/p>\n

(b)\u00a0 BB’ = Minor axis = 2b<\/p>\n

(c)\u00a0 Vertices = (\\(\\pm a\\), 0)<\/p>\n

(d)\u00a0 Latus rectum LL’ = L1L1′ = \\(2a^2\\over b\\), equation x = \\(\\pm\\)ae<\/p>\n

(e)\u00a0 Ends of latus rectum are : L(ae, \\(b^2\\over a\\)), L'(ae, -\\(b^2\\over a\\)), L1(-ae, \\(b^2\\over a\\)), L1′(-ae, -\\(b^2\\over a\\))<\/p>\n

(f)\u00a0 Equation of directrix y = \\(\\pm a\\over e\\)<\/p>\n

(g)\u00a0 Eccentricity : e = \\(\\sqrt{1 – {b^2\\over a^2}}\\)<\/p>\n

(h)\u00a0 Foci : S = (ae, 0) & S’ = (-ae, 0)<\/p>\n

\u00a0<\/p>\n

(b) \u00a0Second type of Ellipse<\/strong> is<\/p>\n

\n

\\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1 (a < b)<\/p>\n<\/blockquote>\n

\"ellipse1<\/p>\n

\u00a0<\/p>\n

(a)\u00a0 AA’ = Minor axis = 2a<\/p>\n

(b)\u00a0 BB’ = Major axis = 2b<\/p>\n

(c)\u00a0 Vertices = (0, \\(\\pm b\\))<\/p>\n

(d)\u00a0 Latus rectum LL’ = L1L1′ = \\(2a^2\\over b\\), equation y = \\(\\pm\\)be<\/p>\n

(e)\u00a0 Ends of latus rectum are : L(\\(a^2\\over b\\), be), L'(-\\(a^2\\over b\\), be), L1(\\(a^2\\over b\\), -be), L1′(-\\(a^2\\over b\\), -be)<\/p>\n

(f)\u00a0 Equation of directrix y = \\(\\pm b\\over e\\)<\/p>\n

(g)\u00a0 Eccentricity : e = \\(\\sqrt{1 – {a^2\\over b^2}}\\)<\/p>\n

(h)\u00a0 Foci : S = (0, be) & S’ = (0, -be)<\/p>\n

Line and an ellipse<\/strong><\/h4>\n

The line y = mx + c meets the ellipse \\({x_1}^2\\over a^2\\) + \\({y_1}^2\\over b^2\\) = 1 in two real, coincident, or imaginary according as \\(c^2\\) is < = or > \\(a^2m^2 + b^2\\).<\/p>\n

Hence y = mx + c is tangent to the ellipse \\({x_1}^2\\over a^2\\) + \\({y_1}^2\\over b^2\\) = 1 if \\(c^2\\) = \\(a^2m^2 + b^2\\)<\/p>\n

\n

Related Questions<\/h3>\n

The foci of an ellipse are \\((\\pm 2, 0)\\) and its eccentricity is 1\/2, find its equation.<\/a><\/p>\n

Find the equation of the ellipse whose axes are along the coordinate axes, vertices are \\((0, \\pm 10)\\) and eccentricity e = 4\/5.<\/a><\/p>\n

If the foci of a hyperbola are foci of the ellipse \\(x^2\\over 25\\) + \\(y^2\\over 9\\) = 1. If the eccentricity of the hyperbola be 2, then its equation is :<\/a><\/p>\n\n\n

\n
Next – Equation of Tangent to Ellipse in all Forms<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Equation of Ellipse in Standard Form<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here, you will learn different types of ellipse and their basic definitions with their graphs. Let’s begin – Different Types of Ellipse (a)\u00a0 First type of Ellipse is \\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1, where a > b \u00a0 (a)\u00a0 AA’ = Major axis = 2a (b)\u00a0 BB’ = Minor axis = 2b (c)\u00a0 …<\/p>\n

Different Types of Ellipse Equations and Graph<\/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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[24],"tags":[333,336,335,339,338,334,337],"yoast_head":"\nDifferent Types of Ellipse Equations and Graph<\/title>\n<meta name=\"description\" content=\"In this post you will learn different types of ellipse and their basic definitions with their graphs.\" \/>\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\/different-types-of-ellipse\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Different Types of Ellipse Equations and Graph\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn different types of ellipse and their basic definitions with their graphs.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/different-types-of-ellipse\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-08-10T12:51:27+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-02-16T16:20:28+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathemerize.com\/wp-content\/uploads\/2021\/07\/ellipse.png\" \/>\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=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/different-types-of-ellipse\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/different-types-of-ellipse\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Different Types of Ellipse Equations and Graph\",\"datePublished\":\"2021-08-10T12:51:27+00:00\",\"dateModified\":\"2022-02-16T16:20:28+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/different-types-of-ellipse\/\"},\"wordCount\":355,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"different types of ellipse\",\"eccentricity of ellipse\",\"foci of ellipse\",\"graphs of ellipse\",\"horizontal ellipse\",\"types of ellipse equation\",\"vertical ellipse\"],\"articleSection\":[\"Ellipse\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/different-types-of-ellipse\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/different-types-of-ellipse\/\",\"url\":\"https:\/\/mathemerize.com\/different-types-of-ellipse\/\",\"name\":\"Different Types of Ellipse Equations and Graph\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-08-10T12:51:27+00:00\",\"dateModified\":\"2022-02-16T16:20:28+00:00\",\"description\":\"In this post you will learn different types of ellipse and their basic definitions with their graphs.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/different-types-of-ellipse\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/different-types-of-ellipse\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/different-types-of-ellipse\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Different Types of Ellipse Equations and Graph\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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