Question

If the line $lx+my=1$ be a tangent to the circle $x^2+y^2=a^2$, prove that the point $(l,m)$ lies on a circle.

Answer 1

Condition of tangency gives $l^2+m^2=1/a^2$ and hence the point $(l,m)$ lies on the circle $x^2+y^2=1/a^2$.