# Ellipses

## 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.