The ellipse is a slightly generalized form of the circle. A further generalization is an egg-shape. The generating equation for an ellipse with foci at` (sqrt(a`^{2}-b^{2}),0) and` (-sqrt(a`^{2}-b^{2}),0) having 'radius' 2*a is:

**x**^{2}/a^{2}+y^{2}/b^{2}=1

Below I have included a sketch of an ellipse.

,....onOK@@@@@@@@@@@HQme....,
,..szSZSZF'` | `'TUXUXux..,
,zrP'` `'Gcc,
,xw'` \'--, | `'wx,
.u'` \ `--_ `'n.
,dy` \ '--, | `qb,
/7` \ `--_ r2 b `A\
4y` r1\ '--, | \D
,I' \ `--_ `U,
dp \ |'--, qb
,j' \ `--_ `t,
AV \ | '--, VA
69- - - - - - - - - - -O- - - - - - - - - - - -O- -a- - - - - - - - -96
VA (focus) | (focus) AV
`t, ,j'
qb | dp
`I, ,U'
\D | 4y`
VA, /7`
`qb, | ,dy`
`'n. .u'`
`'xw, | ,mx'`
`'Gcc, ,zzN'`
``'Tuxuxux., | ,.szszszF'``
````'TTOK@@@@@@@@@@@HQTT'````

The points on the edge of the ellipse can alse be described as those points p where `r1+r2 = 2*a`, with r1 measured as 'the distance from p to one focus' and r2 measured as 'the distance from p to the other focus'. (Unfortunately, the 'ellipse' above isn't quite right proportionally, but it should be enough to give a general idea.)

Some properties of the ellipse: