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.

Table 1. Ellipse Features From an Equation

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.