Different Types of Ellipse Equations and Graph<\/a><\/p>\nExample<\/strong><\/span> : For the given ellipses, find the equation of directrix.<\/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
The eccentricity of ellipse (e) = \\(\\sqrt{1 – {b^2\\over a^2}}\\)<\/p>\n
e = \\(\\sqrt{1 – 16\/25}\\) = \\(3\\over 5\\)<\/p>\n
Now, the equation of directrix is x = \\(a\\over e\\) and x = \\(-a\\over e\\)<\/p>\n
\\(\\implies\\) x = \\(25\\over 3\\) and x = \\(-25\\over 3\\)<\/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
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
Since, center of this ellipse is (1, 0)<\/p>\n
Therefore, the equation of directrix is x = \\(a\\over e\\) + h and x = \\(-a\\over e\\) + h<\/p>\n
\\(\\implies\\) x = \\(2\\over \\sqrt{3}\\) + 1 and y = \\(-2\\over \\sqrt{3}\\) + 1<\/p>\n
Note<\/strong> : For the ellipse \\((x – h)^2\\over a^2\\) + \\((y – k)^2\\over b^2\\) = 1 with center (h. k),<\/p>\n(i)<\/strong> For ellipse a > b,<\/p>\nThe equation of directrix is x = \\(a\\over e\\) + h and x = \\(-a\\over e\\) + h<\/p><\/blockquote>\n
(ii)<\/strong> For ellipse a < b,<\/p>\nThe equation of directrix is y = \\(b\\over e\\) + k and y = \\(-b\\over e\\) + k<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
Here you will learn what is the formula to find the equation of directrix of ellipse with examples. Let’s begin – Directrix of Ellipse Equation (i) For the ellipse \\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1, a > b The equation of directrix is x = \\(a\\over e\\) and x = \\(-a\\over e\\) (ii) For …<\/p>\n
Directrix of Ellipse – Equation and Formula<\/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":"\nDirectrix of Ellipse - Equation and Formula<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the formula to find the equation of directrix of ellipse 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\/directrix-of-ellipse-equation-and-formula\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Directrix of Ellipse - 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