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 Math Help > Geometry > Circles, Conic Sections > Ellipse Reflection Property

# The Ellipse Reflection Property

This elegant proof comes from website http://www.ies.co.jp/math/java/conics/focus_ellipse/focus_ellipse.html

 If the interior of ellipse is silvered to produce a mirror, rays originated at ellipse's focus are reflected to the other focus of the ellipse.

## Proof

 Part 1. Point P is a point on the ellipse, which is defined as the locus of points R such that AR+BR is a constant. L is a tangent line of the ellipse at point P. Point Q moves on L. If Q = P, AQ + BQ = minimum. Part 2. There are two point A, B, a line L and a moving point Q on L.  Point A' is the reflection of A about L. When AQ + BQ = minimum at Q = P, BQ and QA' form BA', which is a straight line. Angles made by AP, BP and L are equal to each other.

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