8. The parabola \(C\) has equation \(y ^ { 2 } = 4 a x\), where \(a\) is a positive constant.
The point \(P \left( a p ^ { 2 } , 2 a p \right)\) lies on the parabola \(C\).
- Show that an equation of the normal to \(C\) at \(P\) is
$$y + p x = a p ^ { 3 } + 2 a p$$
The normal to \(C\) at the point \(P\) meets the \(x\)-axis at the point \(( 6 a , 0 )\) and meets the directrix of \(C\) at the point \(D\). Given that \(p > 0\),
- find, in terms of \(a\), the coordinates of \(D\).
Given also that the directrix of \(C\) cuts the \(x\)-axis at the point \(X\),
- find, in terms of \(a\), the area of the triangle XPD, giving your answer in its simplest form.