{"id":6882,"date":"2021-10-21T21:56:51","date_gmt":"2021-10-21T16:26:51","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6882"},"modified":"2021-10-25T09:51:02","modified_gmt":"2021-10-25T04:21:02","slug":"if-x-4y-5-0-and-4x-ky-7-0-are-two-perpendicular-lines-then-k-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-x-4y-5-0-and-4x-ky-7-0-are-two-perpendicular-lines-then-k-is\/","title":{"rendered":"If x + 4y &#8211; 5 = 0 and 4x + ky + 7 = 0 are two perpendicular lines then k is"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>\\(m_1\\) = -\\(1\\over 4\\)\u00a0 \\(m_2\\) = -\\(4\\over k\\)<\/p>\n<p>Two lines are perpendicular if \\(m_1 m_2\\) = -1<\/p>\n<p>\\(\\implies\\)\u00a0 (-\\(1\\over 4\\))\\(\\times\\)(-\\(4\\over k\\)) = -1\u00a0 \\(\\implies\\)\u00a0 k = -1<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/if-the-straight-line-3x-4y-5-kx-y-3-0-is-parallel-to-y-axis-then-the-value-of-k-is\/\" aria-label=\"\u201cIf the straight line 3x + 4y + 5 \u2013 k(x + y + 3) = 0 is parallel to y-axis, then the value of k is\u201d (Edit)\">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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/if-the-line-2x-y-k-passes-through-the-point-which-divides-the-line-segment-joining-the-points-11-and-24-in-the-ratio-32-then-k-is-equal-to\/\" aria-label=\"\u201cIf 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\u201d (Edit)\">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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/the-slope-of-tangent-parallel-to-the-chord-joining-the-points-2-3-and-3-4-is\/\" aria-label=\"\u201cThe slope of tangent parallel to the chord joining the points (2, -3) and (3, 4) is\u201d (Edit)\">The slope of tangent parallel to the chord joining the points (2, -3) and (3, 4) is<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/find-the-equation-of-lines-which-passes-through-the-point-34-and-the-sum-of-intercepts-on-the-axes-is-14\/\" aria-label=\"\u201cFind the equation of lines which passes through the point (3,4) and the sum of intercepts on the axes is 14.\u201d (Edit)\">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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/if-p-is-the-length-of-the-perpendicular-from-the-origin-to-the-line-xover-a-yover-b-1-then-prove-that-1over-p2-1over-a2-1over-b2\/\" aria-label=\"\u201cIf 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\\)\u201d (Edit)\">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":"<p>Solution : \\(m_1\\) = -\\(1\\over 4\\)\u00a0 \\(m_2\\) = -\\(4\\over k\\) Two lines are perpendicular if \\(m_1 m_2\\) = -1 \\(\\implies\\)\u00a0 (-\\(1\\over 4\\))\\(\\times\\)(-\\(4\\over k\\)) = -1\u00a0 \\(\\implies\\)\u00a0 k = -1 Similar Questions If the straight line 3x + 4y + 5 \u2013 k(x + y + 3) = 0 is parallel to y-axis, then the value &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/if-x-4y-5-0-and-4x-ky-7-0-are-two-perpendicular-lines-then-k-is\/\"> <span class=\"screen-reader-text\">If x + 4y &#8211; 5 = 0 and 4x + ky + 7 = 0 are two perpendicular lines then k 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":[43,48],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If x + 4y - 5 = 0 and 4x + ky + 7 = 0 are two perpendicular lines then k 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\/if-x-4y-5-0-and-4x-ky-7-0-are-two-perpendicular-lines-then-k-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If x + 4y - 5 = 0 and 4x + ky + 7 = 0 are two perpendicular lines then k is\" \/>\n<meta property=\"og:description\" content=\"Solution : (m_1) = -(1over 4)\u00a0 (m_2) = -(4over k) Two lines are perpendicular if (m_1 m_2) = -1 (implies)\u00a0 (-(1over 4))(times)(-(4over k)) = -1\u00a0 (implies)\u00a0 k = -1 Similar Questions If the straight line 3x + 4y + 5 \u2013 k(x + y + 3) = 0 is parallel to y-axis, then the value &hellip; 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