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Math Help - ellipse

  1. #1
    Member Veronica1999's Avatar
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    ellipse

    The figure at right shows one of the many rectangles that can be inscribed in the ellipse 4x2 + 9y2 = 36. The first-quadrant corner of this rectangle is (1.8, 1.6). Find the dimensions of the inscribed rectangle that has the largest area. It is not the one shown.

    I am using quess and check now.
    Is there a smarter approach?
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  2. #2
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    Re: ellipse

    Quote Originally Posted by Veronica1999 View Post
    The figure at right shows one of the many rectangles that can be inscribed in the ellipse 4x2 + 9y2 = 36. The first-quadrant corner of this rectangle is (1.8, 1.6). Find the dimensions of the inscribed rectangle that has the largest area. It is not the one shown.

    I am using quess and check now.
    Is there a smarter approach?
    (a) start by solving the ellipse equation for y in terms of x.

    (b) graph the equation A = xy (substituting what you got for y in part (a)) for the area of the rectangle in quad I.

    (c) locate the maximum on the graph.
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