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Math Help - Optimazation Ellipse

  1. #1
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    Optimazation Ellipse

    Find the area of the largest rectangle that can be inscribed in the ellipse
    x^2 / a^2   + y^2 / b^2 = 1

    All I have so far is that the area = 4xy
    Not sure where to go next; too many variables.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Remember that a and b are constants.
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  3. #3
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    Since the corners of the rectangle are on the ellipse, the "x" and "y" in xy must satisfy x^2/a^2+ y^2/b^2= 1. As Unknown008 said, a and b are constants not variables. You can either write y= b\sqrt{1- x^2/a^2} or differentiate xy with respect to x: y+ xy'= 0, and get y' by differentiating x^2/a^2+ y^2/b^2= 1 implicitely.
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