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    Math Games
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    Equation of an Ellipse

    Standard Form equation

    Worksheet Version of this Web page (same questions on a worksheet)
    Related:
    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 = 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?
    Answer
    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

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