12.3 Ellipses

Ideas in this lesson

Centers and axes

The larger squared denominator lies along the major axis. Both squared terms have positive signs.

Vertices and covertices

Move from the center by each corresponding semiaxis length along its coordinate axis.

Covertices

Move from the center along the minor axis by the minor semiaxis in both directions.

Foci

For an ellipse, the squared focal distance equals major semiaxis squared minus minor semiaxis squared.

Write an ellipse equation

Use the center and the horizontal and vertical semiaxis lengths as squared denominators.