Square $ABCD$ has side length $60$. An ellipse $E$ is circumscribed about the square and there is a point $P$ on the ellipse such that $PC = PD =50$. What is the area of $E$? (You may assume the sides

Square $ABCD$ has side length $60$. An ellipse $E$ is circumscribed about the square and there is a point $P$ on the ellipse such that $PC = PD =50$. What is the area of $E$? (You may assume the sides of the square are parallel to the axes of the ellipse.)