A rectangle is to be inscribed in the ellipse (x^2/4)+y^2=1 What should the dimensions of the rectangle be to maximize its area? What is the maximum area?
Added by Edward G.
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The rectangle is inscribed in the ellipse, so its corners will touch the ellipse. Therefore, the coordinates of the corners of the rectangle will satisfy the equation of the ellipse. We can take one corner in the first quadrant (x, y) without loss of generality. Show more…
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