Rectangle in an Ellipse

Geometry Level 3

\(ABCD\) is a rectangle whose vertices lie on the circumference of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\).

Let \(P\) is the maximum area of \(ABCD\) and \(Q\) is the area of the ellipse. Then the value of \(\frac{P}{Q}\) can be written as \(\frac{n}{\pi}\). Find \(n\).

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