{"id":6914,"date":"2021-10-21T22:34:23","date_gmt":"2021-10-21T17:04:23","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6914"},"modified":"2021-10-25T01:12:47","modified_gmt":"2021-10-24T19:42:47","slug":"the-slope-of-the-line-touching-both-the-parabolas-y2-4x-and-x2-32-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-slope-of-the-line-touching-both-the-parabolas-y2-4x-and-x2-32-is\/","title":{"rendered":"The slope of the line touching both the parabolas \\(y^2\\) = 4x and \\(x^2\\) = -32 is"},"content":{"rendered":"

Solution :<\/h2>\n

for parabola, \\(y^2\\) = 4x<\/p>\n

Let y = mx + \\(1\\over m\\) is tangent line and it touches the parabola \\(x^2\\) = -32.<\/p>\n

\\(\\therefore\\) \\(x^2\\) = -32(mx + \\(1\\over m\\))<\/p>\n

\\(\\implies\\) \\(x^2 + 32mx + {32\\over m}\\) = 0<\/p>\n

Now, D = 0 because it touches the curve.<\/p>\n

\\(\\therefore\\) \\((32m)^2 – 4.{32\\over m}\\) = 0<\/p>\n

\\(\\implies\\) \\(m^3\\) = \\(1\\over 8\\)<\/p>\n

\\(\\implies\\)\u00a0 m = \\(1\\over 2\\)<\/p>\n

\n

Similar Questions<\/h3>\n

What is the equation of common tangent to the parabola \\(y^2\\) = 4ax and \\(x^2\\) = 4ay ?<\/a><\/p>\n

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

Find the equation of the tangents to the parabola \\(y^2\\) = 9x which go through the point (4,10).<\/a><\/p>\n

Find the value of k for which the point (k-1, k) lies inside the parabola \\(y^2\\) = 4x.<\/a><\/p>\n

The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x \u2013 4y + 3 = 0 is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : for parabola, \\(y^2\\) = 4x Let y = mx + \\(1\\over m\\) is tangent line and it touches the parabola \\(x^2\\) = -32. \\(\\therefore\\) \\(x^2\\) = -32(mx + \\(1\\over m\\)) \\(\\implies\\) \\(x^2 + 32mx + {32\\over m}\\) = 0 Now, D = 0 because it touches the curve. \\(\\therefore\\) \\((32m)^2 – 4.{32\\over m}\\) …<\/p>\n

The slope of the line touching both the parabolas \\(y^2\\) = 4x and \\(x^2\\) = -32 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":"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":"\nThe slope of the line touching both the parabolas \\(y^2\\) = 4x and \\(x^2\\) = -32 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-slope-of-the-line-touching-both-the-parabolas-y2-4x-and-x2-32-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The slope of the line touching both the parabolas \\(y^2\\) = 4x and \\(x^2\\) = -32 is\" \/>\n<meta property=\"og:description\" content=\"Solution : for parabola, (y^2) = 4x Let y = mx + (1over m) is tangent line and it touches the parabola (x^2) = -32. 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