Question

The tangents drawn from the origin to the circle $x^2+y^2-2rx-2hy+h^2=0$ are perpendicular then sum of all possible values of $\frac{h}{r}$ is ___

Answer 1

Combined equation of the tangents drawn from (0, 0)to the circle is

$(x^2+y^2-2rx-2hy+h^2)h^2=(-rx-hy+h^2{)}^2$ here coefficient of $x^2+$ coefficient of $y^2=0\Rightarrow (h^2-r^2)+(h^2-h^2)=0$

$\Rightarrow \frac{h}{r}=\pm 1$