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. |
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Proof
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Part 1.
Point P is a point on the ellipse.
L is a tangent line of the ellipse at point P.
Point Q moves on L.
If Q = P , AQ + BQ = minimum.
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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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Related
pages in this website
Summary
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