{"id":37035,"date":"2022-12-01T10:26:15","date_gmt":"2022-12-01T04:56:15","guid":{"rendered":"https:\/\/tsboardsolutions.com\/?p=37035"},"modified":"2022-12-01T10:26:15","modified_gmt":"2022-12-01T04:56:15","slug":"ts-inter-1st-year-maths-1b-transformation-of-axes-formulas","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.com\/ts-inter-1st-year-maths-1b-transformation-of-axes-formulas\/","title":{"rendered":"TS Inter 1st Year Maths 1B Transformation of Axes Formulas"},"content":{"rendered":"<p>Learning these <a href=\"https:\/\/tsboardsolutions.com\/ts-inter-1st-year-maths-1B-formulas\/\">TS Inter 1st Year Maths 1B Formulas<\/a> Chapter 2 Transformation of Axes will help students to solve mathematical problems quickly.<\/p>\n<h2>TS Inter 1st Year Maths 1B Transformation of Axes Formulas<\/h2>\n<p>\u2192 The transformation obtained, by shifting the origin to a given different point in the plane without changing the directions of coordinate axes therein is called a Translation of axes.<br \/>\nIf the origin is shifted to (h, k) by translation of axes, then<\/p>\n<ul>\n<li>The coordinates of a point P(x, y) are transformed as P(x &#8211; h, y &#8211; k) and<\/li>\n<li>The equation f(x, y) = 0 of the curve is transformed as f(X + h. Y + k) = 0<\/li>\n<\/ul>\n<p>\u2192 The transformation obtained, by rotating both the coordinate axes in the plane by an equal angle, without changing the position of the origin is called a Rotation of axes.<br \/>\nx = X cos \u03b8 &#8211; Y sin \u03b8, X = x cos \u03b8 &#8211; y sin \u03b8<br \/>\ny = X sin \u03b8 + Y cos \u03b8, Y = &#8211; x sin \u03b8 + y cos \u03b8<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/10\/TS-Board-Solutions.png\" alt=\"TS Inter 1st Year Maths 1B Transformation of Axes Formulas\" width=\"183\" height=\"15\" \/><\/p>\n<p>\u2192 To make the first degree terms absent, origin should be shifted to \\(\\left(\\frac{h f-b g}{a b-h^2}, \\frac{g h-a f}{a b-h^2}\\right)\\)<\/p>\n<p>\u2192 To make xy term to be absent, axes should be rotated through an angle 0 given by tan 2\u03b8 = \\(\\frac{2 h}{a-b}\\)<br \/>\n\u21d2 \u03b8 = \\(\\frac{1}{2}\\)tan<sup>-1<\/sup>\\(\\left(\\frac{2 h}{a-b}\\right)\\)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Learning these TS Inter 1st Year Maths 1B Formulas Chapter 2 Transformation of Axes will help students to solve mathematical problems quickly. TS Inter 1st Year Maths 1B Transformation of Axes Formulas \u2192 The transformation obtained, by shifting the origin to a given different point in the plane without changing the directions of coordinate axes &#8230; <a title=\"TS Inter 1st Year Maths 1B Transformation of Axes Formulas\" class=\"read-more\" href=\"https:\/\/tsboardsolutions.com\/ts-inter-1st-year-maths-1b-transformation-of-axes-formulas\/\" aria-label=\"More on TS Inter 1st Year Maths 1B Transformation of Axes Formulas\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[27],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>TS Inter 1st Year Maths 1B Transformation of Axes Formulas - TS Board Solutions<\/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:\/\/tsboardsolutions.com\/ts-inter-1st-year-maths-1b-transformation-of-axes-formulas\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"TS Inter 1st Year Maths 1B Transformation of Axes Formulas - TS Board Solutions\" \/>\n<meta property=\"og:description\" content=\"Learning these TS Inter 1st Year Maths 1B Formulas Chapter 2 Transformation of Axes will help students to solve mathematical problems quickly. 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