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Good Links
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Fun Games
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Interactive
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Good Links
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Scientific Calc
Algebra
Fun Games
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Interactive
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Good Links
Home
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Scientific Calc
Algebra
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Trigonometry
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Equation of an Ellipse

Standard Form equation

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 major axis is the segment that contains both foci and has its endpoints on the ellipse. These endpoints are called the vertices. The midpoint of major axis is the center of the ellipse.
The minor axis is perpendicular to the major axis at the center, and the endpoints of the minor axis are called co-vertices.
The vertices are at the intersection of the major axis and the ellipse.
The co-vertices are at the intersection of the minor axis and the ellipse.


You can think of an ellipse as an oval.

Picture of an Ellipse


Picture of an ellipse

  Standard Form Equation of an Ellipse  



The general form for the standard form equation of an ellipse is

Horizontal Major Axis Example

    Example of the graph and equation of an ellipse on the cartesian plane
  • The major axis of this ellipse is horizontal and is the red segment from (-2,0) to (2,0)
  • The center of this ellipse is the origin since (0,0) is the midpoint of the major axis
  • The value of a = 2 and b = 1




Vertical Major Axis Example

    Example of the graph and equation of an ellipse on the cartesian plane
  • The major axis of this ellipse is vertical and is the red segment from (2,0) to (-2,0)
  • The center of this ellipse is the origin since (0,0) is the midpoint of the major axis
  • The value of a = 2 and b = 1
Can you determine the values of a and b for the equation of the ellipse pictured below?
Answer
Practice Problem equation of ellipse
Can you determine the values of a and b for the equation of the ellipse pictured in the graph below?
Answer
Practice Problem equation of ellipse
What are values of a and b for the standard form equation of the ellipse in the graph ?
Answer
Practice Problem three  equation of ellipse
Examine the graph of the ellipse belo to determine a and b for the standard form equation?
Answer
Practice Problem four  equation of ellipse
Examine the graph of the ellipse belo to determine a and b for the standard form equation?
Answer
Practice Problem five  equation of ellipse
What is the standard form equation of the ellipse in the graph below?
Answer
Practice Problem six  equation of ellipse
What is the standard form equation of the ellipse in the graph below?
Answer
Practice Problem seven  equation of ellipse
  Graph of Ellipse from the Equation  
The problems below provide practice creating the graph of an ellipse from the equation of the ellipse. 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?
Answer
Can you graph the equation of the ellipse below ? WHat are the values of a and b?
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Can you graph the equation of the ellipse below ? WHat are the values of a and b?
Answer
Determine the values of a and b as well as what the graph of the ellipse with the equation shown below.
Answer
Determine the values of a and b as well as what the graph of the ellipse with the equation shown below.
Answer
Determine the values of a and b as well as what the graph of the ellipse with the equation shown below.
Answer
Determine the values of a and b as well as what the graph of the ellipse with the equation shown below.
Answer
Determine the values of a and b as well as what the graph of the ellipse with the equation shown below.
Answer
Determine the values of a and b as well as what the graph of the ellipse with the equation shown below.
Answer