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Math Help - How do you find parametric equations for an ellipse?

  1. #1
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    How do you find parametric equations for an ellipse?

    For example, how would I find the parametric equations for (x^2)/(25) + (y^2)/(81) = 1
    Last edited by mr fantastic; October 21st 2009 at 05:18 PM. Reason: Restored deleted question.
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  2. #2
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    Quote Originally Posted by jamessmith View Post
    For example, how would I find the parametric equations for (x^2)/(25) + (y^2)/(81) = 1

    An ellipse is really just a stretched circle right?

    Well the most common parameterization for a circle is

    x=a\cos(t)
    y=a\sin(t)

    where "a" is the radius of the circle

    So if we wanna stretch it, we look at your equation. The biggest value that x takes on is 5 and the biggest value of y is 9

    So the radii are \sqrt{5} and 3

    So this time we just make the parameterization

    x=a\cos(t)
    y=b\sin(t)

    with a=5 and b=9
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  3. #3
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    Quote Originally Posted by jamessmith View Post
    For example, how would I find the parametric equations for (x^2)/(25) + (y^2)/(81) = 1

    x=5\cos t\,,\,\,y=9\sin t\,,\,\,0\leq t \leq 2\pi

    Tonio
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