Area between the parabolas \(y^{2}=4ax\) and \(x^{2}=4ay\) is

\(\frac{4}{3}a^{2}\) \(\frac{8}{3}a^{2}\) \(4a\) \(\frac{16}{3}a^{2}\)

\(\frac{16}{3}a^{2}\)

\(\begin{aligned}\text{Area}&=\int_{0}^{4a}\left(2\sqrt{ax}-\frac{x^{2}}{4a}\right)dx\\ &=\frac{16}{3}a^{2}\end{aligned}\)