{"id":2544,"date":"2021-07-12T13:00:18","date_gmt":"2021-07-12T13:00:18","guid":{"rendered":"https:\/\/mathemerize.com\/?p=2544"},"modified":"2021-11-24T23:31:39","modified_gmt":"2021-11-24T18:01:39","slug":"equation-of-conjugate-hyperbola","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/equation-of-conjugate-hyperbola\/","title":{"rendered":"Equation of Conjugate Hyperbola"},"content":{"rendered":"

Here you will learn what is conjugate hyperbola, equation of conjugate hyperbola and basic definitions of like eccentricity and latus rectum.<\/p>\n

Let’s begin –<\/p>\n

What is Conjugate Hyperbola ?<\/h2>\n

The hyperbola whose transverse & conjugate axes are respectively the conjugate and transverse axes of given hyperbola is called the conjugate hyperbola of given hyperbola.\u00a0<\/p>\n

The equation of the conjugate hyperbola<\/strong> of the hyperbola \\(x^2\\over a^2\\) – \\(y^2\\over b^2\\) = 1 is<\/p>\n

\n

-\\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1.<\/p>\n<\/blockquote>\n

The graph of the conjugate hyperbola is shown in figure.<\/p>\n

The eccentricity of the conjugate hyperbola<\/strong> is given by \\(a^2\\) = \\(b^2(e^2-1)\\) and the length of latus rectum<\/strong> is \\(2a^2\\over b\\).<\/p>\n

Conjugate Hyperbola & Basic Definitions :<\/h2>\n

The equation of the conjugate hyperbola is -\\(x^2\\over a^2\\) + \\(y^2\\over b^2\\) = 1.\"conjugate<\/strong><\/p>\n

(a) Centre (0,0).<\/p>\n

(b) Vertices (0,b) & (0,-b)<\/p>\n

(c) foci \\((0, \\pm ae)\\)<\/p>\n

(d) Length of\u00a0 transverse axis is 2b<\/p>\n

(e) Length of\u00a0 conjugate axis is 2a<\/p>\n

(f) Equation of\u00a0 directrices is x = \\(\\pm {b\\over e}\\)<\/p>\n

(g) Eccentricity is given by \\(a^2\\) = \\(b^2(e^2-1)\\)<\/p>\n

(h) Length of latus rectum is \\(2a^2\\over b\\).<\/p>\n

(i) Equation of the transverse axis is x = 0.<\/p>\n

(j) Equation of the conjugate axis is y = 0.<\/p>\n\n\n

Example : <\/span> Find the eccentricity of the conjugate hyperbola to the hyperbola \\(x^2 – 3y^2\\) = 1.\n<\/p>

Solution : <\/span>Equation of the conjugate hyperbola to the hyperbola \\(x^2 – 3y^2\\) = 1 is \\(-x^2 + 3y^2\\) = 1\n\\(\\implies\\) -\\(x^2\\over 1\\) + \\(y^2\\over 1\/3\\) = 1.

\nHere \\(a^2\\) = 1, \\(b^2\\) = 1\/3

\nTherefore eccentricity is e = \\(\\sqrt{1 + a^2\/b^2}\\) = 2.<\/p>\n\n\n

Hope you learnt conjugate hyperbola, learn more concepts of hyperbola and practice more questions to get ahead in the competition. Good luck!<\/p>\n\n\n

\n
Next – Parametric Equation of Rectangular Hyperbola<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Equation of the Hyperbola – Graph of a Hyperbola<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is conjugate hyperbola, equation of conjugate hyperbola and basic definitions of like eccentricity and latus rectum. Let’s begin – What is Conjugate Hyperbola ? The hyperbola whose transverse & conjugate axes are respectively the conjugate and transverse axes of given hyperbola is called the conjugate hyperbola of given hyperbola.\u00a0 The …<\/p>\n

Equation of Conjugate 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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[25],"tags":[399,397,385,398],"yoast_head":"\nEquation of Conjugate Hyperbola - Mathemerize<\/title>\n<meta name=\"description\" content=\"Learn what is conjugate hyperbola, equation of conjugate hyperbola and basic definitions of like eccentricity and latus rectum here.\" \/>\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\/equation-of-conjugate-hyperbola\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equation of Conjugate Hyperbola - 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