Focus and Directrix of Ellipse

In the presence of a point F and a straight line d, ellipse can be characterized is the locus of points P whose distances to F and d are in a fixed ratio less than 1: dist(P, F) / dist(P, d) = const < 1. The point is called a focus and the line a directrix of the ellipse. This property is often taken for a definition of ellipse.

illustration of definition of ellipse via eccentricity

For every ellipse there are two focus/directrix combinations. The line joining the foci is the axis of summetry of the ellipse and is perpendicular to both directrices.

Below is an interactive illustration. Drag the point on the ellipse to see how the distances to a focus or directrix change.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

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Conic Sections > Ellipse

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