{"id":3434,"date":"2021-07-24T13:14:43","date_gmt":"2021-07-24T13:14:43","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3434"},"modified":"2021-11-20T22:39:29","modified_gmt":"2021-11-20T17:09:29","slug":"equation-of-normal-to-circle","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/equation-of-normal-to-circle\/","title":{"rendered":"Equation of Normal to a Circle with Examples"},"content":{"rendered":"

The normal at a point is the straight line which is perpendicular to the tangent to circle at the point of contact. Normal at a point of the circle passes through the center of circle. Here, you will learn how to find equation of normal to a circle with example.<\/p>\n

Equation of Normal to a Circle :<\/h2>\n

(a) Equations of normal at point (\\(x_1, y_1\\)) of circle \\({x}^2 + {y}^2 + 2gx + 2fy + c\\) = 0 is<\/p>\n

\n

y – \\(y_1\\) = (\\(y_1 + f\\over {x_1 + g}\\))(\\(x – x_1\\))<\/strong><\/p>\n<\/blockquote>\n

(b) The equations of normal on any point (\\(x_1, y_1\\)) of circle \\(x^2\\) + \\(y^2\\) = \\(a^2\\) is<\/p>\n

\n

\\(y\\over x\\) = \\(y_1\\over x_1\\)<\/strong><\/p>\n<\/blockquote>\n

(c) If \\(x^2\\) + \\(y^2\\) = \\(a^2\\) is the equation of the circle then at any point ‘t’ of this circle (acost, asint)<\/strong>, the equation of normal is <\/p>\n

\n

xsint – ycost = 0<\/strong><\/p>\n<\/blockquote>\n\n\n

Example : <\/span> Find the normal to the circle \\(x^2 + y^2\\) = 0 at the point (1, 2).<\/p>\n

Solution : <\/span>We have, \\(x^2 + y^2\\) = 0

\nSince normal on any point (\\(x_1, y_1\\)) of circle \\(x^2\\) + \\(y^2\\) = \\(a^2\\) is \\(y\\over x\\) = \\(y_1\\over x_1\\).

\ni.e. \\(y\\over x\\) = \\(2\\over 1\\)

\n\\(\\implies\\) y = 2x

\nwhich is the required normal to circle.

<\/p>\n\n\n\n

Example : <\/span> Find the normal to the circle \\(x^2 + y^2 – 5x + 2y – 48\\) = 0 at the point (5, 6).<\/p>\n

Solution : <\/span>We have, \\(x^2 + y^2 – 5x + 2y – 48\\) = 0

\nSince the normal to the circle always passes through center so equation of the normal will be the line passing through (5,6) & (\\(5\\over 2\\), -1)

\ni.e. y + 1 = \\(7\\over {5\/2}\\)(x – \\(5\\over 2\\)) \\(\\implies\\) 5y + 5 = 14x – 35

\n\\(\\implies\\) 14x – 5y – 40 = 0

\nwhich is the required normal to circle.

<\/p>\n\n\n\n

\n
Next – Common Tangent to Two Circles \u2013 Direct & Transverse<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Equation of Tangent to a Circle \u2013 Condition of Tangency<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

The normal at a point is the straight line which is perpendicular to the tangent to circle at the point of contact. Normal at a point of the circle passes through the center of circle. Here, you will learn how to find equation of normal to a circle with example. Equation of Normal to a …<\/p>\n

Equation of Normal to a Circle with Examples<\/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":[23],"tags":[181,187,188],"yoast_head":"\nEquation of Normal to a Circle with Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post, you will learn how to find equation of normal to circle in point form and parametric form with examples.\" \/>\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-normal-to-circle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equation of Normal to a Circle with Examples - 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