MathDB

Focal Radii and Ellipse Tangent

Source: VTRMC 2022 P2

January 4, 2023

VTRMCcollege contestsellipse

Problem Statement

Let

A

and

B

be the two foci of an ellipse and let

P

be a point on this ellipse. Prove that the focal radii of

P

(that is, the segments

\overline{AP}

and

\overline{BP}

) form equal angles with the tangent to the ellipse at

P