
Related:
 Equation of Ellipse
 Major Axis of Ellipse
 Minor Axis of Ellipse
 Vertices
 Covetices
 focus of an ellipse
 Is a circle an ellipse?
 Eccentricty of Ellipse
 area of an ellipse
 Orbits of Planets as ellipses
 Translate ellipse
 images
 Worksheet Version of this Web page (same questions on a worksheet)
Formula for the focus of an Ellipse
An ellipse is the set of all points in a plane such that the sum of the distances from T to two fixed points F_{1} and F_{2} is a given constant, K. TF_{1} + TF_{2} = K
F_{1} and F_{2} are both foci (plural of focus) of the ellipse.
The formula generally associated with the focus of an ellipse is c²= a² − b² where c is the distance from the focus to vertex and b is the distance from the vertex a covetex on the minor axis
Example of Focus
The special case of a circle
A circle is a special case of an ellipse. Analogous to the fact that a square is a kind of rectangle, a circle is a special case of an ellipse. In terms of the focus, a circle is an ellipse in which the two foci are in the same spot so, in true, the two foci are the same point.
Practice Problems
Focus of Ellipse from the Equation
The problems below provide practice finding the focus of an ellipse from the ellipse's equation.
All practice problems on this page have the ellipse centered at the origin.