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Q.
The locus of a point whose chord of contact with respect to the circle $x^{2}+y^{2}=4$ is a tangent to the hyperbola $x y=1$ is a/an
Conic Sections
Solution:
Let the point be $(h, k)$.
Then the equation of the chord of contact is $h x+k y=4$.
Since $h x+k y=4$ is tangent to $x y=1$,
$x\left(\frac{4-h x}{k}\right)=1$
has two equal roots. Therefore,
$h x^{2}-4 x+k=0$
or $ h k=4$
Thus, the locus of $(h, k)$ is $x y=4$. Hence,
$c^{2}=4$