Question

If locus of a point, whose chord of contact with respect to the circle $x^2+y^2=4$ is a tangent to the hyperbola $xy=1$ is $xy=c^2$, then value of $c^2=$

Answer 1

Let the point be $(h,k)$ .
Then equation of the chord of contact is
$hx+ky=4$

any tangent to $xy=1$ is
$\frac{x}{t}+yt=2$
on comparison, we get
$\frac{2}{t}=h,2t=k\Rightarrow kh=4$
Hence locus will be
$xy=4$
$\therefore c^2=4$