# Definition and Equations of an Ellipse

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This Demonstration illustrates the definition of an ellipse, the canonical and parametric equations of the ellipse, and the effect of eccentricity on the shape of an ellipse.

Contributed by: V. Tomilenko (June 2015)

Open content licensed under CC BY-NC-SA

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## Details

Given two points, and (the foci), an ellipse is the locus of points such that the sum of the distances from to and is a constant.

To get equations, choose a Cartesian coordinate system as follows: 1. the axis is directed along the line passing through the foci and ; 2. the origin is taken to be the midpoint of the segment ; 3. the foci and are separated by a distance .

If the sum of the distances from a point on an ellipse to the two foci is , then and are the major and minor semiaxes of the ellipse.

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