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Find the equation of tangent for the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$ in parametric form?

$\begin{array}{1 1}(a)\;\large\frac{x\sec\theta}{a^2}+\frac{y\tan \theta}{b}\normalsize =1\\(b)\;\large\frac{x\sec\theta}{a}-\frac{y\tan \theta}{b}\normalsize =1\\(c)\;\large\frac{x\tan\theta}{a^2}+\frac{y\sec \theta}{b}\normalsize =1\\(d)\;\text{None of these}\end{array}$

1 Answer

We know the parametric co-ordinate of the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$ is $(a\sec\theta,b\tan\theta)$
And also we know
Equation of tangent for the hyperbola is $\large\frac{xx_1}{a^2}-\frac{yy_1}{b^2}$$=1$
Replacing $(x_1,y_1)$ by $(a\sec\theta,b\tan \theta)$
$\large\frac{x\sec\theta}{a}-\frac{y\tan \theta}{b}\normalsize =1$
Hence (b) is the correct answer.
answered Feb 10, 2014 by sreemathi.v

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