## Ellipses

An ellipse is a stretched circle.

The longest diameter, `$PQ$`

, is called the major axis. The shortest diameter, `$RS$`

, is called the minor axis. The major and
minor axes are always perpendicular.

An ellipse can be defined by the parameters `$a$`

and `$b$`

, where the major axis has length `$2a$`

and the minor axis has length
`$2b$`

(or vice versa). An ellipse centred on the origin with its major and minor axes aligned with the x and y axes looks like this:

The ellipse crosses the x axis at points (a, 0) and (-a, 0). It crosses the y axis at points (0, b) and (0, -b).

A circle is a special case of an ellipse, where the major and minor axes have the same length.