Common Ellipse Features
The standard form of the equation for an ellipse is as follows.
Ellipses have the following features.
Two foci and two directrices
Eccentricity less than 1
Two axes of symmetry
Major axis: the longer axis of symmetry, containing the foci
Minor axis: the shorter axis of symmetry
Two vertices: the endpoints of the major axis
Two covertices: the endpoints of the minor axis
Center: intersection of the major and minor axes
The directrices are parallel to the minor axis.
We can divide ellipses into two types, depending on whether a or b is bigger.
The information we can find from the equation of each type of ellipse is summarized in the table below.
Graphs of Ellipses
Use the sliders below to change the values of a, b, h, and k, and see the different ellipses that result.
The ellipse is graphed along with its foci, directrices, and major axis.