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# Find the parametric form of tangent for the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}=$$1 \begin{array}{1 1}(a)\;\large\frac{x\cos \theta}{a}+\frac{y\sin \theta}{b}\normalsize=1\\(b)\;\large\frac{x\cos \theta}{a}-\frac{y\sin \theta}{b}\normalsize=1\\(c)\;\large\frac{x\cos \theta}{a}+\frac{y\sin \theta}{b}\normalsize=0\\(d)\;\text{None of these}\end{array} Can you answer this question? ## 1 Answer 0 votes Parametric coordinates of the ellipse, \large\frac{x^2}{a^2}+\frac{y^2}{b^2} are (a\cos \theta,b\sin \theta) Equation of tangent to the ellipse at (x_1,y_1) is \large\frac{xx_1}{a^2}+\frac{yy_1}{b^2}$$=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.
edited Mar 27, 2014