{"id":8107,"date":"2021-11-13T23:11:32","date_gmt":"2021-11-13T17:41:32","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8107"},"modified":"2021-11-14T00:34:38","modified_gmt":"2021-11-13T19:04:38","slug":"find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2\/","title":{"rendered":"Find the slope of normal to the curve x = 1 – \\(a sin\\theta\\), y = \\(b cos^2\\theta\\) at \\(\\theta\\) = \\(\\pi\\over 2\\)."},"content":{"rendered":"

Solution :<\/h2>\n

We have, x = 1 – \\(a sin\\theta\\), y = \\(b cos^2\\theta\\)<\/p>\n

\\(\\implies\\)\u00a0 \\(dx\\over d\\theta\\) = \\(-a cos\\theta\\)\u00a0 and \\(dy\\over d\\theta\\) = \\(-2b cos\\theta sin\\theta\\)<\/p>\n

\\(\\therefore\\)\u00a0 \\(dy\\over dx\\) = \\(dy\/d\\theta\\over dx\/d\\theta\\) = \\(2b\\over a\\) \\(sin\\theta\\)<\/p>\n

\\(\\implies\\)\u00a0 \\(dy\\over dx\\)\u00a0 at \\(\\pi\\over 2\\) = \\(2b\\over a\\)<\/p>\n

Hence, Slope of normal<\/a> at \\(\\theta\\) = \\(\\pi\\over 2\\) = \\(-a\\over 2b\\)<\/p>\n

\n

Similar Questions<\/h3>\n

Find the slope of the normal to the curve x = \\(a cos^3\\theta\\), y = \\(a sin^3\\theta\\) at \\(\\theta\\) = \\(\\pi\\over 4\\).<\/a><\/p>\n

Show that the tangents to the curve y = \\(2x^3 \u2013 3\\) at the points where x =2 and x = -2 are parallel.<\/a><\/p>\n

Find the equations of the tangent and the normal at the point \u2018t\u2019 on the curve x = \\(a sin^3 t\\), y = \\(b cos^3 t\\).<\/a><\/p>\n

Find the equation of the normal to the curve y = \\(2x^2 + 3 sin x\\) at x = 0.<\/a><\/p>\n

Find the angle between the curves xy = 6 and \\(x^2 y\\) =12.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We have, x = 1 – \\(a sin\\theta\\), y = \\(b cos^2\\theta\\) \\(\\implies\\)\u00a0 \\(dx\\over d\\theta\\) = \\(-a cos\\theta\\)\u00a0 and \\(dy\\over d\\theta\\) = \\(-2b cos\\theta sin\\theta\\) \\(\\therefore\\)\u00a0 \\(dy\\over dx\\) = \\(dy\/d\\theta\\over dx\/d\\theta\\) = \\(2b\\over a\\) \\(sin\\theta\\) \\(\\implies\\)\u00a0 \\(dy\\over dx\\)\u00a0 at \\(\\pi\\over 2\\) = \\(2b\\over a\\) Hence, Slope of normal at \\(\\theta\\) = \\(\\pi\\over 2\\) …<\/p>\n

Find the slope of normal to the curve x = 1 – \\(a sin\\theta\\), y = \\(b cos^2\\theta\\) at \\(\\theta\\) = \\(\\pi\\over 2\\).<\/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":"\nFind the slope of normal to the curve x = 1 - \\(a sin\\theta\\), y = \\(b cos^2\\theta\\) at \\(\\theta\\) = \\(\\pi\\over 2\\).<\/title>\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\/find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the slope of normal to the curve x = 1 - \\(a sin\\theta\\), y = \\(b cos^2\\theta\\) at \\(\\theta\\) = \\(\\pi\\over 2\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : We have, x = 1 – (a sintheta), y = (b cos^2theta) (implies)\u00a0 (dxover dtheta) = (-a costheta)\u00a0 and (dyover dtheta) = (-2b costheta sintheta) (therefore)\u00a0 (dyover dx) = (dy\/dthetaover dx\/dtheta) = (2bover a) (sintheta) (implies)\u00a0 (dyover dx)\u00a0 at (piover 2) = (2bover a) Hence, Slope of normal at (theta) = (piover 2) … Find the slope of normal to the curve x = 1 – (a sintheta), y = (b cos^2theta) at (theta) = (piover 2). Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-11-13T17:41:32+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-11-13T19:04:38+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\/find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Find the slope of normal to the curve x = 1 – \\\\(a sin\\\\theta\\\\), y = \\\\(b cos^2\\\\theta\\\\) at \\\\(\\\\theta\\\\) = \\\\(\\\\pi\\\\over 2\\\\).\",\"datePublished\":\"2021-11-13T17:41:32+00:00\",\"dateModified\":\"2021-11-13T19:04:38+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2\/\"},\"wordCount\":180,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Application of Derivatives Questions\",\"Maths Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2\/\",\"url\":\"https:\/\/mathemerize.com\/find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2\/\",\"name\":\"Find the slope of normal to the curve x = 1 - 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\\(a sin\\theta\\), y = \\(b cos^2\\theta\\) at \\(\\theta\\) = \\(\\pi\\over 2\\).","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\/find-the-slope-of-normal-to-the-curve-x-1-a-sintheta-y-b-cos2theta-at-theta-piover-2\/","og_locale":"en_US","og_type":"article","og_title":"Find the slope of normal to the curve x = 1 - \\(a sin\\theta\\), y = \\(b cos^2\\theta\\) at \\(\\theta\\) = \\(\\pi\\over 2\\).","og_description":"Solution : We have, x = 1 – (a sintheta), y = (b cos^2theta) (implies)\u00a0 (dxover dtheta) = (-a costheta)\u00a0 and (dyover dtheta) = (-2b costheta sintheta) (therefore)\u00a0 (dyover dx) = (dy\/dthetaover dx\/dtheta) = (2bover a) (sintheta) (implies)\u00a0 (dyover dx)\u00a0 at (piover 2) = (2bover a) Hence, Slope of normal at (theta) = (piover 2) … Find the slope of normal to the curve x = 1 – (a sintheta), y = (b cos^2theta) at (theta) = (piover 2). 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