JEE Coordinate (4)!

Consider the parabola $y^2 = 4x$ .

Let $P$ and $Q$ be two points $(4,-4)$ and $(9,6)$ on the parabola.

Let $R$ be a moving point on the arc of the parabola between $P$ and $Q$ .

Find the maximum possible area of $RPQ$ .

If maximum area is $S$ , report your answer as $(4S)^{1/3}$ .

This is a part of my set practice for jee 2017