Editing Focus (geometry) (section)

===Defining conics in terms of two foci===
[[File:locating_the_foci_of_an_ellipse.svg|thumb|The foci of an ellipse (purple crosses) are at intersects of the [[major axis]] (red) and a circle (cyan) of [[radius]] equal to the [[semi-major axis]] (blue), centred on an end of the minor axis (grey)]]
An [[ellipse]] can be defined as the [[locus (mathematics)|locus]] of points for which the sum of the distances to two given foci is constant.

A [[circle]] is the special case of an ellipse in which the two foci coincide with each other. Thus, a circle can be more simply defined as the locus of points each of which is a fixed distance from a single given focus.  A circle can also be defined as the [[Circles of Apollonius|circle of Apollonius]], in terms of two different foci, as the locus of points having a fixed ratio of distances to the two foci.

A [[parabola]] is a limiting case of an ellipse in which one of the foci is a [[point at infinity]].

A [[hyperbola]] can be defined as the locus of points for which the [[absolute value]] of the difference between the distances to two given foci is constant.