A circle of radius is concentric with the ellipse

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

A circle of radius rr is concentric with the ellipse x2a2+y2b2=1\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⁡−1r2−b2a2−r2.\tan^{-1} \sqrt{\frac{r^2 - b^2}{a^2 - r^2}}.

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