Falzoon's Ellipse

Calculus Level 4

A circle and an ellipse of the same area share the interior of a larger circle, without overlap.

For the size of the smaller circle, the ellipse has the largest possible area that could fit in the space between the smaller and larger circle. Let \(a\) be the combined areas of the ellipse and the small circle, and let \(b\) be the area of the large circle.

Find \(\left\lfloor 10000\dfrac { a }{ b } \right\rfloor \)

You may want to use a computer for this.

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