# Area of a pillow

Geometry Level 5

The graphs of four identical parabolas, as shown above, intersect at the points $$\: (5,5), \:(-5,5), \:(-5,-5)$$ and $$(5,-5)$$. The vertices of these parabolas are all $$4$$ units away from the origin, and the area enclosed by the quadrilateral whose vertices are the foci of these parabolas is $$\frac{1681}{16}$$ square units.

If the area formed about the origin enclosed by the four parabolas can be expressed in the form $$\frac{A}{B}$$, where $$A$$ and $$B$$ are coprime positive integers, determine $$A+B$$.

Details and Assumptions:

1. The parabolas are identical in the sense that they have the same focal lengths.
×