Reflection property of ellipse

The line segments connecting any point on an ellipse to the two foci make equal angles to the tangent line at that point.

In symbols, if the ellipse has foci F and G, then for any point P on the ellipse, if QR is the line tangent to the ellipse at P, then angle QPF equals angle RPG .

The property is called the reflection property because it implies that a ray of light or a sound wave emanating from one focus will reflect off the curve to the other focus.

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Last updated: 10 June, 2008

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