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 F1 and F2 is a given constant, K. TF1 + TF2 = K
F1 and F2 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 co-vetex 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.
Focus of Ellipse from the Equation
The problems below provide practice finding the focus of an ellipse from the ellipse's quation.
All practice problems on this page have the ellipse centered at the origin.