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Graphing Calc
Scientific Calc
Algebra
Fun Games
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Interactive
Trigonometry
Good Links
Home
Graphing Calc
Scientific Calc
Algebra
Fun Games
Geometry
Interactive
Trigonometry
Good Links

Focus of Ellipse

Formula for Focus of 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

Formula for the focus of an Ellipse


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

Use the formula for the focus to determine the coordinates either focus
Answer
Practice problem for Focus
Determine the coordinates of each focus of the ellipse below
Answer
Finding focus of ellipse
Use the values of a and b below to determine the value of c and the coordinates of the focus?
Answer
focus of ellipse problem 3
Use the values of a and b below to determine the value of c and the coordinates of the focus?
Answer
Practice Problem four focus of ellipse
  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?
equation of focus one
Answer
Can you graph the equation of the ellipse below ? WHat are the values of a and b?
Answer