powered by Google (TM)
index: click on a letter
A B C D E
F G H  I  J
K L M N O
P Q R S T
U V W X Y
Z A to Z index
index: subject areas
numbers & symbols
sets, logic, proofs
geometry
algebra
trigonometry
advanced algebra
& pre-calculus
calculus
advanced topics
probability &
statistics
real world
applications
multimedia
entries
about mathwords  
website feedback  


Focal Radius

This term has distinctly different definitions for different authors.

Usage 1: For some authors, this refers to the distance from the center to the focus for either an ellipse or a hyperbola. This definition of focal radius is usually written c.

Usage 2: For other authors, focal radius refers to the distance from a point on a conic section to a focus. In this case the focal radius varies depending where the point is on the curve (unless the conic in question is a circle). If there are two foci then there are two focal radii.

Note: Using this second definition, the sum of the focal radii of an ellipse is a constant. It is the same as the length of the major diameter. The difference of the focal radii of a hyperbola is a constant. It is the distance between the vertices.

 

Movie clip


Ellipse: Sum of the focal radii (usage 2) is constant

(182K)

 

See also

Foci of an ellipse, foci of a hyperbola, focus of a parabola

 


  this page updated 19-jul-17
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
Copyright © 2000 by Bruce Simmons
All rights reserved
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes