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Find the parametric form of tangent for the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}=$$1$

$\begin{array}{1 1}(a)\;\large\frac{x\cos \theta}{a}+\frac{y\sin \theta}{b}\normalsize=1\\(b)\;\large\frac{x\cos \theta}{a}-\frac{y\sin \theta}{b}\normalsize=1\\(c)\;\large\frac{x\cos \theta}{a}+\frac{y\sin \theta}{b}\normalsize=0\\(d)\;\text{None of these}\end{array}$

1 Answer

Parametric coordinates of the ellipse, $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$ are $(a\cos \theta,b\sin \theta)$
Equation of tangent to the ellipse at $ (x_1,y_1)$ is $\large\frac{xx_1}{a^2}+\frac{yy_1}{b^2}$$=1$
Where $(x_1,y_1)$ is $(a\cos \theta,b\sin \theta)$
Hence the equation of the tangent becomes
$\large\frac{x\cos \theta}{a}+\frac{y\sin \theta}{b}\normalsize=1$
Hence (a) is the correct answer.
answered Feb 6, 2014 by sreemathi.v
edited Mar 27, 2014 by rvidyagovindarajan_1

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