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Focus of EllipseFormula for Focus of EllipseFree Math Printable Worksheets : :  Worksheet Version of this Web page (same questions on a worksheet)Related: Equation of Ellipse | Major Axis of Ellipse| Minor Axis of Ellipse|Vertices| Co-vetices | focus of an ellipse | Is a circle an ellipse? | Eccentricty of Ellipse | area of an ellipse | Orbits of Planets as ellipses | Translate ellipse | images
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 = KF1 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 Formula for the focus of an Ellipse
Example of Focus
The special case of a circle
Practice Problems
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.
Use the formula for the focus to determine the coordinates either focus
Determine the coordinates of each focus of the ellipse below
Use the values of a and b below to determine the value of c and the coordinates of the focus?
Use the values of a and b below to determine the value of c and the coordinates of the 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.
Can you graph the equation of the ellipse below and find the values of a and b?
Can you graph the equation of the ellipse below ? WHat are the values of a and b?
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