6. The parabola \(C\) has equation \(y ^ { 2 } = 16 x\).
- Verify that the point \(P \left( 4 t ^ { 2 } , 8 t \right)\) is a general point on \(C\).
- Write down the coordinates of the focus \(S\) of \(C\).
- Show that the normal to \(C\) at \(P\) has equation
$$y + t x = 8 t + 4 t ^ { 3 }$$
The normal to \(C\) at \(P\) meets the \(x\)-axis at the point \(N\).
- Find the area of triangle \(P S N\) in terms of \(t\), giving your answer in its simplest form.