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Focus of a Parabola

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

A parabola is defined as follows: For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.

Note: For a parabolic mirror, all rays of light emitting from the focus reflect off the parabola and travel parallel to each other (parallel to the axis of symmetry as well).

 



 

Example:  

This is a graph of the parabola with all its major features labeled: axis of symmetry, focus, vertex, and directrix.

 

 

See also

Conic sections, foci of an ellipse, foci of a hyperbola, focal radius

 


  this page updated 21-feb-16
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes