Focus

Pronunciation: /ˈfoʊ kəs/ Explain

An ellipse, a hyperbola, and a parabola with a common focus.
Figure 1: Focus Image courtesy Seahen.

In geometry, a focus is a point related to the construction and properties of conic sections. A circle and a parabola have one focus. The focus of a circle is also center of the circle. Sometimes, it is convenient to talk of a circle having two coincidental focuses, meaning two focuses that occupy the same point. Similarly, a parabola is sometimes considered to have a second focus at infinity. An ellipse and a hyperbola both have two focuses.

References

  1. Hustler, James Devereux. The Elements of the Conic Sections with the Sections of the Conoids. 3rd edition. pp 1-18. www.archive.org. J. Deighton and Sons. 1826. Last Accessed 8/6/2018. http://www.archive.org/stream/elementsofconics00hastuoft#page/1/mode/1up/search/focus. Buy the book
  2. Loomis, Elias. Elements of geometry and conic sections. www.archive.org. Harper & Brother, Publishers. 1849. Last Accessed 8/6/2018. http://www.archive.org/stream/elementsgeometr05loomgoog#page/n183/mode/1up/search/focus. Buy the book

More Information

  • McAdams, David E.. Circle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/c/circle.html.

Cite this article as:

McAdams, David E. Focus. 7/11/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/focus.html.

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Revision History

7/9/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/7/2010: Added "References". (McAdams, David E.)
10/11/2008: Initial version. (McAdams, David E.)

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