An ellipse can be defined as the locus of points for each of which the sum of the distances to two given foci is a 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 circle of Apollonius, in terms of two different foci, as the set 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 each of which the absolute value of the difference between the distances to two given foci is a constant.

It is also possible to describe all conic sections in terms of a single focus and a single directrix, which is a given line not containing the focus. A conic is defined as the locus of points for each of which the distance to the focus divided by the distance to the directrix is a fixed positive constant, called the eccentricity *e*. If *e* is between zero and one the conic is an ellipse; if *e*=1 the conic is a parabola; and if *e*>1 the conic is a hyperbola. If the distance to the focus is fixed and the directrix is a line at infinity, so the eccentricity is zero, then the conic is a circle.

This page was last edited on 15 July 2016, at 05:11 (UTC).

Reference: https://en.wikipedia.org/wiki/Focus_(geometry) under CC BY-SA license.

Reference: https://en.wikipedia.org/wiki/Focus_(geometry) under CC BY-SA license.

- Geometry
- UK
- /ËfoÊkaÉª/
- US
- /ËfoÊsaÉª/
- Curves
- Conic Sections
- Circle
- Ellipse
- Parabola
- Hyperbola
- Cassini Oval
- Cartesian Oval
- N-ellipse
- Locus
- Circle Of Apollonius
- Point At Infinity
- Directrix
- Line At Infinity

- Amoeba Music
- Focus (geometry)
- American Working Class
- Altopiano Delle Murge
- Alex Inglethorpe
- Lovelock Correctional Center
- Albany-Colonie Yankees
- Shire Of Burdekin
- Garden History Society
- Al Purdy
- Lucrezia D%27Este (1535-1598)
- Admont
- Lucinda, Queensland
- Adolphus William Ward
- A133 Road
- 5th U-boat Flotilla
- 4th Field Artillery Regiment
- 4%C3%97400 Meters Relay
- 2016 Rio Olympics
- Adam Wenceslaus, Duke Of Cieszyn
- 2006 FIFA Club World Cup Squads
- Alabama River
- 2014%E2%80%9315 Portland Pilots Men%27s Basketball Team
- 1998%E2%80%9399 Detroit Pistons Season
- Department Of The Shenandoah
- Department Of Washington
- 1986 Castrol 500
- 1965 African Cup Of Nations
- Joseph K. Mansfield
- 1934 Michigan Wolverines Football Team