An ellipse has two focus points. The word foci (pronounced 'foe-sigh') is the plural of 'focus'. One focus, two foci.

The foci always lie on the major (longest) axis, spaced equally each side of the center. If the major axis and minor axis are the same length, the figure is a circle and both foci are at the center. Reshape the ellipse above and try to create this situation. An ellipse is defined in part by the location of the foci. However if you have an ellipse with known major and minor axis lengths, you can find the location of the foci using the formula below

where F  is the distance from each focus to the center (see figure above) j  is the semi-major axis (major radius) n  is the semi-minor axis (minor radius)

In the figure above, drag any of the four orange dots. This will change the length of the major and minor axes. You will see how the foci move and the calculation will change to reflect their new location.

If the inside of an ellipse is a mirror, a light ray leaving one focus will always pass through the other. For more on this see Optical Properties of Elliptical Mirrors