Constant ratio property of ellipses

For any non-circular ellipse there is a positive constant e < 1 (called the eccentricity ), and there are a point (called a focus ) and a line (called a directrix ), such that the ellipse is the set of all points in the plane of the focus and directrix the ratio of whose distances to the focus and to the directrix is e.

In other words, an ellipse is a set of points the ratio of whose distances from a fixed point and a fixed line is a constant between 0 and 1.

An ellipse has two foci and two corresponding directrices. The constant ratio property applies to either pair.

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Last updated: 10 June, 2008

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