Focus

Pronunciation: /ˈfoʊ kəs/ ?

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. A ellipse and a hyperbola both have two focuses.

References

  1. focus. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=focus&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Author unknown. The Elements of the Conic Sections with the Sections of the Conoids, 3rd ed., pp 1-18. Published by J. Deighton and Sons, 1826. (Accessed: 2010-01-07). http://www.archive.org/stream/elementsofconics00hastuoft#page/1/mode/1up/search/focus.
  3. Loomis, Elias. Elements of geometry and conic sections. Harper & Brother, Publishers, 1849. (Accessed: 2010-02-04). http://www.archive.org/stream/elementsgeometr05loomgoog#page/n183/mode/1up/search/focus.

More Information

  • McAdams, David. Circle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Circle.
  • McAdams, David. Hyperbola. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Hyperbola.
  • McAdams, David. Parabola. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Parabola.

Printed Resources

Cite this article as:


Focus. 2010-01-07. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/focus.html.

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2010-01-07: Added "References" (McAdams, David.)
2008-10-11: Initial version (McAdams, David.)

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