Focus of Ellipse

Formula and exmaples for Focus of Ellipse

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

Picture and formula focus of ellipse

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

Problem 1

Use the formula for the focus to determine the coordinates either focus

Practice problem for Focus
Problem 2

Determine the coordinates of each focus of the ellipse below

Practice problem for Focus
Problem 3

Use the values of a and b below to determine the value of c and the coordinates of the focus?

Practice problem for Focus
Problem 4

Use the values of a and b below to determine the value of c and the coordinates of the focus?

Practice problem for Focus

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.

Click here for practice problems involving an ellipse not centered at the origin.
Problem 5

Can you graph the equation of the ellipse below and find the values of a and b?

equation of focus one
Problem 6

Can you graph the equation of the ellipse below ? WHat are the values of a and b?