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March 28, 2017

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Find the standard equation of an ellipse with the given characteristics and sketch the graph.
Vertices at (0,-5), and (0,5); Foci at (0,-4)and (0,4).

  • Math/Algebra - ,

    The ellipse is centred at the origin (0,0).

    The standard formula for the ellipse is then
    x²/a²+y²/b²=1
    where
    2a=distance between vertices on the major axis
    =(5-(-5)=10, so
    a=5

    Distance between foci
    2c=(4-(-4))=8
    so
    c=4

    To find b, we use the relation
    a²=b²+c²
    or
    5²=b²+4²
    b=sqrt(25-16)=3

    So the equation for the given ellipse is
    x²/5²+y²/3²=1

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