Elliptical Area

An ellipse is centered at the origin. Let $A$ and $B$ be the horizontal and vertical radii lengths of the ellipse, respectively. Assume that $A,B\sim \text{Exp}(1)$ and are independent. Recall that the area of an ellipse with radii $a$ and $b$ is given by $\pi ab$. A circle with diameter $A$ is created as well. Find the probability the area of the circle is larger than the area of the ellipse.