The constant sum property of an ellipse

For any ellipse, there is a positive constant a, and there are two (perhaps coincident) points in the plane (called the foci) such that the ellipse is the set of all points the sum of whose distances to the foci is 2a.

In other words, an ellipse is the set of points the sum of whose distances from the two foci is constant.

If the two foci coincide, then the ellipse is a circle with radius a.

http://www.augsburg.edu/depts/math/MATtours/ellipses1.03.0.html

Last updated: 24 November 1996

MATtours project team led by Larry Copes