Question

Locus of the point of intersection of the pair of perpendicular tangents to the circles $x^{2}+y^{2}=1$ and $x^{2}+$ $y^{2}=7$ is the director circle of the circle with radius equal to

Answer 1

$h^{2}+k^{2}=1+7$
$\therefore $ locus of the point $P$ is
$x^{2}+y^{2}=8$
This is the director circle of circle $x^{2}+y^{2}=4$
$\therefore x^{2}+y^{2}=8$
is director circle of a circle with radius $=2$.