A Date in the Polar Coordinate System (Part 3)

Calculus Level 4

Part 1

Part 2

Rebecca, on the other hand, thinks the best (Answer to Part 1) (which has equation \(r=k+k\sin\theta\) for some \(k<0\)) is the unique one that has equal perimeter and area. This one has a \(k\) value equal to \(\dfrac{-X}{Y\pi}\). Find \(X+Y.\)

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