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Parabolas, ellipses, and hyperbolas, oh my! Learn about this eccentric bunch of shapes.

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In the above diagram, a rectangle \(ABCD\) is inscribed in the ellipse \(\displaystyle{\frac{x^2}{36}+\frac{y^2}{100}=1}.\) What is the maximum area of rectangle \( ABCD?\)

**Note:** The above diagram is not drawn to scale.

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