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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Coordinate Geometry
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Find the parametric form of normal for the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$?

$\begin{array}{1 1}(a)\;\large\frac{ax}{\cos\theta}-\frac{by}{\sin \theta}\normalsize =a^2-b^2\\(b)\;\large\frac{ax}{\cos\theta}-\frac{by}{\sin \theta}\normalsize =a^2+b^2\\(c)\;\large\frac{ax}{\sin\theta}-\frac{by}{\cos \theta}\normalsize =a^2-b^2\\(d)\;\text{None of these}\end{array}$

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1 Answer

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Equation of normal at $(x_1,y_1)$ is
$\large\frac{a^2x}{x_1}-\frac{b^2y}{y_1}$$=a^2-b^2$
Parametric coordinate $(x_1,y_1)$ is $(a\cos\theta,b\sin\theta)$
Hence $\large\frac{a^2x}{a\cos \theta}-\frac{b^2y}{b\sin \theta}$$=a^2-b^2$
$\large\frac{ax}{\cos\theta}-\frac{by}{\sin \theta}\normalsize =a^2-b^2$
Hence (a) is the correct answer.
answered Feb 7, 2014 by sreemathi.v
 

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