4. The parabola \(C\) has cartesian equation \(y ^ { 2 } = 12 x\)
The point \(P \left( 3 p ^ { 2 } , 6 p \right)\) lies on \(C\), where \(p \neq 0\)
- Show that the equation of the normal to the curve \(C\) at the point \(P\) is
$$y + p x = 6 p + 3 p ^ { 3 }$$
This normal crosses the curve \(C\) again at the point \(Q\).
Given that \(p = 2\) and that \(S\) is the focus of the parabola, find - the coordinates of the point \(Q\),
- the area of the triangle \(P Q S\).