# 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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