Different Types of Parabola Equations<\/a><\/p>\nExample<\/span><\/strong> : For the given parabola, find the coordinates of the foci :<\/p>\n(i) \\(y^2\\) = 8x<\/p>\n
(ii) \\(x^2\\) = -16y<\/p>\n
Solution<\/strong><\/span> :<\/p>\n(i) The given parabola is of the form \\(y^2\\) = 4ax, where 4a = 8 i.e. a = 2.<\/p>\n
Hence, the coordinates of the focus are (a, 0) i.e. (2, 0).<\/p>\n
(ii) The given parabola is of the form \\(x^2\\) = -4ay, where 4a = 16 i.e. a = 4.<\/p>\n
Hence, the coordinates of the focus are (0, -a) i.e. (0, -4).<\/p>\n
Example<\/span><\/strong> : Find the coordinates of foci of the parabola \\(y^2 – 8y – x + 19\\) = 0<\/p>\nSolution<\/strong><\/span> : The given equation is<\/p>\n\\(y^2 – 8y – x + 19\\) = 0 \\(\\implies\\) \\(y^2 – 8y\\) = x – 19<\/p>\n
\\(\\implies\\) \\(y^2 – 8y + 16\\) = x – 19 + 16<\/p>\n
\\(\\implies\\) \\((y – 4)^2\\) = (x – 3)<\/p>\n
The equation is of the form \\((y – k)^2\\) = 4a(x – h),<\/strong><\/p>\nOn Comparing we get,<\/p>\n
4a = 1 i.e. a = 1\/4 and k = 4, h = 3<\/p>\n
Hence, the coordinates of focus is (h + a, k).<\/p>\n
i.e. ((3 + 1\/4), 4) = (13\/4, 4).<\/p>\n","protected":false},"excerpt":{"rendered":"
Here you will learn how to find the focus of parabola with examples. Let’s begin – Focus of Parabola Coordinates (i) For Parabola \\(y^2\\) = 4ax : The coordinates of focus is (a, 0). (ii) For Parabola \\(y^2\\) = -4ax : The coordinates of focus is (-a, 0). (iii) For Parabola \\(x^2\\) = 4ay : …<\/p>\n
Focus of Parabola Coordinates with 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":[12],"tags":[],"yoast_head":"\nFocus of Parabola Coordinates with Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn how to find the focus of parabola formula 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\/focus-of-parabola-coordinates-with-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Focus of Parabola Coordinates with Examples - 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