Definition and Equations of an Ellipse
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.
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.