Mathematics

Problem

A circle of radius

r

is concentric with the ellipse

\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

. Prove that the common tangent is inclined to the major axis at an angle

\tan^{-1} \sqrt{\frac{r^2 - b^2}{a^2 - r^2}}.