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Find the locus of intersection of two perpendicular tangent to the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$?

$\begin{array}{1 1}(a)\;h^2+k^2=a^2-b^2\\(b)\;h^2+k^2=a^2+b^2\\(c)\;h^2-k^2=a^2-b^2\\(d)\;k^2-h^2=a^2-b^2\end{array}$

1 Answer

Let any tangent in terms of slope of hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$ is
It passes through (h,k)
Slope of tangent be $m_1$ & $m_2$
$-1=\large\frac{k^2+b^2}{h^2-a^2}$(tangent are $\perp$)
Hence $h^2+k^2=a^2-b^2$
Hence (a) is the correct answer.
answered Feb 10, 2014 by sreemathi.v

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