{"id":6884,"date":"2021-10-21T21:58:58","date_gmt":"2021-10-21T16:28:58","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6884"},"modified":"2021-10-25T09:49:16","modified_gmt":"2021-10-25T04:19:16","slug":"if-lambda-x2-10xy-12y2-5x-16y-3-0-represents-a-pair-of-straight-lines-then-lambda-is-equal-to","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-lambda-x2-10xy-12y2-5x-16y-3-0-represents-a-pair-of-straight-lines-then-lambda-is-equal-to\/","title":{"rendered":"If \\(\\lambda x^2 – 10xy + 12y^2 + 5x – 16y – 3\\) = 0 represents a pair of straight lines, then \\(\\lambda\\) is equal to"},"content":{"rendered":"

Solution :<\/h2>\n

Comparing with \\(ax^2+2hxy+by^2+2gx+2fy+c\\) = 0<\/p>\n

Here a = \\(\\lambda\\), b = 12, c = -3, f = -8, g = 5\/2, h = -5<\/p>\n

Using condition \\(abc+2fgh-af^2-bg^2-ch^2\\) = 0, we have<\/p>\n

\\(\\lambda\\)(12)(-3) + 2(-8)(5\/2)(-5) – \\(\\lambda\\)(64) – 12(25\/4) + 3(25) = 0<\/p>\n

\\(\\implies\\)\u00a0 -36\\(\\lambda\\) + 200 – 64\\(\\lambda\\) – 75 + 75 = 0<\/p>\n

\\(\\implies\\)\u00a0 100\\(\\lambda\\) = 200<\/p>\n

\\(\\therefore\\)\u00a0 \\(\\lambda\\) = 2<\/p>\n

\n

Similar Questions<\/h3>\n

If the straight line 3x + 4y + 5 \u2013 k(x + y + 3) = 0 is parallel to y-axis, then the value of k is<\/a><\/p>\n

If the line 2x + y = k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then k is equal to<\/a><\/p>\n

If x + 4y \u2013 5 = 0 and 4x + ky + 7 = 0 are two perpendicular lines then k is<\/a><\/p>\n

Find the equation of lines which passes through the point (3,4) and the sum of intercepts on the axes is 14.<\/a><\/p>\n

If p is the length of the perpendicular from the origin to the line \\(x\\over a\\) + \\(y\\over b\\) = 1, then prove that \\(1\\over p^2\\) = \\(1\\over a^2\\) + \\(1\\over b^2\\)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Comparing with \\(ax^2+2hxy+by^2+2gx+2fy+c\\) = 0 Here a = \\(\\lambda\\), b = 12, c = -3, f = -8, g = 5\/2, h = -5 Using condition \\(abc+2fgh-af^2-bg^2-ch^2\\) = 0, we have \\(\\lambda\\)(12)(-3) + 2(-8)(5\/2)(-5) – \\(\\lambda\\)(64) – 12(25\/4) + 3(25) = 0 \\(\\implies\\)\u00a0 -36\\(\\lambda\\) + 200 – 64\\(\\lambda\\) – 75 + 75 = …<\/p>\n

If \\(\\lambda x^2 – 10xy + 12y^2 + 5x – 16y – 3\\) = 0 represents a pair of straight lines, then \\(\\lambda\\) is equal to<\/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":[43,48],"tags":[],"yoast_head":"\nIf \\(\\lambda x^2 - 10xy + 12y^2 + 5x - 16y - 3\\) = 0 represents a pair of straight lines, then \\(\\lambda\\) is equal to<\/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\/if-lambda-x2-10xy-12y2-5x-16y-3-0-represents-a-pair-of-straight-lines-then-lambda-is-equal-to\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If \\(\\lambda x^2 - 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