{"id":8060,"date":"2021-11-13T19:34:19","date_gmt":"2021-11-13T14:04:19","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8060"},"modified":"2021-11-14T00:59:10","modified_gmt":"2021-11-13T19:29:10","slug":"the-angle-of-intersection-between-the-curve-x2-32y-and-y2-4x-at-point-16-8-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-angle-of-intersection-between-the-curve-x2-32y-and-y2-4x-at-point-16-8-is\/","title":{"rendered":"The angle of intersection between the curve \\(x^2\\) = 32y and \\(y^2\\) = 4x at point (16, 8) is"},"content":{"rendered":"

Solution :<\/h2>\n

\\(x^2\\) = 32y\u00a0 \\(\\implies\\)\u00a0 \\(dy\\over dx\\) = \\(x\\over 16\\)\u00a0 \\(\\implies\\)\u00a0 \\(y^2\\) = 4x \\(\\implies\\)\u00a0 \\(dy\\over dx\\) = \\(2\\over y\\)<\/p>\n

\\(\\therefore\\)\u00a0 at\u00a0 (16, 8), \\((dy\\over dx)_1\\) = 1, \\((dy\\over dx)_2\\) = \\(1\\over 4\\)<\/p>\n

So, required angle<\/a> = \\(tan^{-1}({1 – {1\\over 4}\\over 1 + 1({1\\over 4})})\\)<\/p>\n

= \\(tan^{-1}({3\\over 5})\\)<\/p>\n

\n

Similar Questions<\/h3>\n

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Find the equation of the tangent to curve y = \\(-5x^2 + 6x + 7\\)\u00a0 at the point (1\/2, 35\/4).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : \\(x^2\\) = 32y\u00a0 \\(\\implies\\)\u00a0 \\(dy\\over dx\\) = \\(x\\over 16\\)\u00a0 \\(\\implies\\)\u00a0 \\(y^2\\) = 4x \\(\\implies\\)\u00a0 \\(dy\\over dx\\) = \\(2\\over y\\) \\(\\therefore\\)\u00a0 at\u00a0 (16, 8), \\((dy\\over dx)_1\\) = 1, \\((dy\\over dx)_2\\) = \\(1\\over 4\\) So, required angle = \\(tan^{-1}({1 – {1\\over 4}\\over 1 + 1({1\\over 4})})\\) = \\(tan^{-1}({3\\over 5})\\) Similar Questions Find the equations of …<\/p>\n

The angle of intersection between the curve \\(x^2\\) = 32y and \\(y^2\\) = 4x at point (16, 8) is<\/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":[66,43],"tags":[],"yoast_head":"\nThe angle of intersection between the curve \\(x^2\\) = 32y and \\(y^2\\) = 4x at point (16, 8) is<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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