{"id":8366,"date":"2021-11-20T22:56:31","date_gmt":"2021-11-20T17:26:31","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8366"},"modified":"2022-01-31T18:37:03","modified_gmt":"2022-01-31T13:07:03","slug":"what-is-the-equation-of-pair-of-tangents-to-a-circle","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-equation-of-pair-of-tangents-to-a-circle\/","title":{"rendered":"Equation of Pair of Tangents to a Circle"},"content":{"rendered":"

Here you will learn what is the equation of pair of tangents to a circle from an external point with example.<\/p>\n

Let’s begin –<\/p>\n

Equation of Pair of Tangents to a Circle<\/h2>\n

Let the equation of circle S = \\(x^2\\) + \\(y^2\\) – \\(a^2\\) and P(\\(x_1,y_1\\)) is any point outside the circle. From the point we can draw two real and distinct tangent and combine equation of pair of tangents is –<\/p>\n

(\\(x^2\\) + \\(y^2\\) – \\(a^2\\))(\\({x_1}^2\\) + \\({y_1}^2\\) – \\(a^2\\)) = \\(({xx_1 + yy_1 – a^2})^2\\)<\/p>\n

or\u00a0 \\(SS_1 = T^2\\)<\/p>\n

where \\(S_1\\) = \\({x_1}^2\\) + \\({y_1}^2\\) – \\(a^2\\)<\/p>\n

and \\(T^2\\) = \\(({xx_1 + yy_1 – a^2})^2\\)<\/p><\/blockquote>\n

Also Read : Length of Tangent to a Circle Formula From an External Point<\/a><\/p>\n

Example<\/strong><\/span> : Find the equation to the pair of tangents drawn from (4, 10) to the circle \\(x^2 + y^2\\) = 4.<\/p>\n

Solution<\/strong><\/span> : Given that, S = \\(x^2 + y^2\\) = 4 and Point P is (4, 10).<\/p>\n

Then, by using above formula,<\/p>\n

\\(S_1\\) = \\(4^2 + 10^2 – 4\\) = 112<\/p>\n

\\(T^2\\) = \\((4x + 10y – 4)^2\\) =\u00a0 \\((4x + 10y)^2\\) + 16 – 8(4x + 10y)<\/p>\n

= \\(16x^2\\) + \\(100y^2\\) + 80xy + 16 – 32x – 80y<\/p>\n

= \\(16x^2\\) + \\(100y^2\\) – 32x – 80y + 80xy + 16<\/p>\n

Hence, the combined equation of pair of tangents is<\/p>\n

\\(x^2 + y^2 – 4\\)(112) = \\(16x^2\\) + \\(100y^2\\) – 32x – 80y + 80xy + 16<\/p>\n

\\(96x^2\\) + \\(12y^2\\) – 32x – 80y + 80xy – 464 = 0<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the equation of pair of tangents to a circle from an external point with example. Let’s begin – Equation of Pair of Tangents to a Circle Let the equation of circle S = \\(x^2\\) + \\(y^2\\) – \\(a^2\\) and P(\\(x_1,y_1\\)) is any point outside the circle. From the point …<\/p>\n

Equation of Pair of Tangents to a Circle<\/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":[23],"tags":[845,846,847],"yoast_head":"\nEquation of Pair of Tangents to a Circle<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the equation of pair of tangents to a circle from an external point with example.\" \/>\n<meta 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