The Teardrop

Calculus Level 5

Let \(c\) be a negative constant. When the two parabolas \(y=x^2+c\) and \(x=y^2+c\) are tangent, the area of the region of overlap can be expressed as \(\frac {A}B\), where \(A\) and \(B\) are coprime positive integers. Find \(A + B\).