The locus of the intersection of tangents which are at right angles is known as director circle of the hyperbola. The equation to the director circle is :<\/p>\n
\\(x^2+y^2\\) = \\(a^2-b^2\\)<\/p><\/blockquote>\n
If \\(b^2\\) < \\(a^2\\), this circle is real ; If \\(b^2\\) = \\(a^2\\) the radius of the circle is zero & it reduces to a point circle at the origin. In this case the center is the only point from which the tangents at right angles can be drawn to the curve.<\/p>\n
If \\(b^2\\) > \\(a^2\\), the radius of the circle is imaginary, so that there is no such circle & so no tangents at right angle can be drawn to the curve.<\/p>\n","protected":false},"excerpt":{"rendered":"
Solution : The locus of the intersection of tangents which are at right angles is known as director circle of the hyperbola. The equation to the director circle is : \\(x^2+y^2\\) = \\(a^2-b^2\\) If \\(b^2\\) < \\(a^2\\), this circle is real ; If \\(b^2\\) = \\(a^2\\) the radius of the circle is zero & it …<\/p>\n
What is the Equation of Director Circle of Hyperbola ?<\/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":[51,43],"tags":[],"yoast_head":"\nWhat is the Equation of Director Circle of Hyperbola ? - Mathemerize<\/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\/what-is-the-equation-of-director-circle-of-hyperbola\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the Equation of Director Circle of Hyperbola ? - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : The locus of the intersection of tangents which are at right angles is known as director circle of the hyperbola. 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