{"id":6840,"date":"2021-10-21T19:42:57","date_gmt":"2021-10-21T14:12:57","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6840"},"modified":"2021-10-25T01:14:58","modified_gmt":"2021-10-24T19:44:58","slug":"the-length-of-latus-rectum-of-a-parabola-whose-focus-is-2-3-and-directrix-is-the-line-x-4y-3-0-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-length-of-latus-rectum-of-a-parabola-whose-focus-is-2-3-and-directrix-is-the-line-x-4y-3-0-is\/","title":{"rendered":"The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x &#8211; 4y + 3 = 0 is"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>The length of latus rectum = 2 x perpendicular from focus to the directrix<\/p>\n<p>= 2 x |\\({2-4(3)+3}\\over {\\sqrt{1+16}}\\)| = \\(14\\over \\sqrt{17}\\)<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/the-slope-of-the-line-touching-both-the-parabolas-y2-4x-and-x2-32-is\/\" aria-label=\"\u201cThe slope of the line touching both the parabolas \\(y^2\\) = 4x and \\(x^2\\) = -32 is\u201d (Edit)\">The slope of the line touching both the parabolas \\(y^2\\) = 4x and \\(x^2\\) = -32 is<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-locus-of-middle-point-of-the-chord-of-the-parabola-y2-4ax-which-pass-through-a-given-p-q\/\" aria-label=\"\u201cFind the locus of middle point of the chord of the parabola \\(y^2\\) = 4ax which pass through a given (p, q).\u201d (Edit)\">Find the locus of middle point of the chord of the parabola \\(y^2\\) = 4ax which pass through a given (p, q).<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-equation-of-the-tangents-to-the-parabola-y2-9x-which-go-through-the-point-410\/\" aria-label=\"\u201cFind the equation of the tangents to the parabola \\(y^2\\) = 9x which go through the point (4,10).\u201d (Edit)\">Find the equation of the tangents to the parabola \\(y^2\\) = 9x which go through the point (4,10).<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-value-of-k-for-which-the-point-k-1-k-lies-inside-the-parabola-y2-4x\/\" aria-label=\"\u201cFind the value of k for which the point (k-1, k) lies inside the parabola \\(y^2\\) = 4x.\u201d (Edit)\">Find the value of k for which the point (k-1, k) lies inside the parabola \\(y^2\\) = 4x.<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/what-is-the-equation-of-tangent-to-the-parabola-having-slope-m\/\" aria-label=\"\u201cWhat is the equation of tangent to the parabola having slope m?\u201d (Edit)\">What is the equation of tangent to the parabola having slope m?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : The length of latus rectum = 2 x perpendicular from focus to the directrix = 2 x |\\({2-4(3)+3}\\over {\\sqrt{1+16}}\\)| = \\(14\\over \\sqrt{17}\\) Similar Questions The slope of the line touching both the parabolas \\(y^2\\) = 4x and \\(x^2\\) = -32 is Find the locus of middle point of the chord of the parabola &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/the-length-of-latus-rectum-of-a-parabola-whose-focus-is-2-3-and-directrix-is-the-line-x-4y-3-0-is\/\"> <span class=\"screen-reader-text\">The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x &#8211; 4y + 3 = 0 is<\/span> Read More &raquo;<\/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":[43,46],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x - 4y + 3 = 0 is<\/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\/the-length-of-latus-rectum-of-a-parabola-whose-focus-is-2-3-and-directrix-is-the-line-x-4y-3-0-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x - 4y + 3 = 0 is\" \/>\n<meta property=\"og:description\" content=\"Solution : The length of latus rectum = 2 x perpendicular from focus to the directrix = 2 x |({2-4(3)+3}over {sqrt{1+16}})| = (14over sqrt{17}) Similar Questions The slope of the line touching both the parabolas (y^2) = 4x and (x^2) = -32 is Find the locus of middle point of the chord of the parabola &hellip; 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