Find the area of the circle $4x^2 + 4y^2 = 9$ which is interior to the parabola $x^2 = 4y$.

Question

$\begin{array}{1 1}\frac{\sqrt 2}{6}+\frac{9}{4}\sin^{-1}\big( \frac{2\sqrt 2}{3}\big) \\ \frac{\sqrt 2}{3}+\frac{5}{4}\sin^{-1}\big( \frac{\sqrt 2}{3}\big) \\ \frac{\sqrt 2}{3}-\frac{9}{4}\sin^{-1}\big( \frac{2\sqrt 2}{3}\big)\\ \frac{\sqrt 2}{6}+\frac{9}{4}\cos^{-1}\big( \frac{2\sqrt 2}{3}\big)\end{array}$