7. The parabola \(C\) has equation \(y ^ { 2 } = 4 a x\), where \(a\) is a constant and \(a > 0\) The point \(Q \left( a q ^ { 2 } , 2 a q \right) , q > 0\), lies on the parabola \(C\).
- Show that an equation of the tangent to \(C\) at \(Q\) is
$$q y = x + a q ^ { 2 }$$
The tangent to \(C\) at the point \(Q\) meets the \(x\)-axis at the point \(X \left( - \frac { 1 } { 4 } a , 0 \right)\) and meets the directrix of \(C\) at the point \(D\).
- Find, in terms of \(a\), the coordinates of \(D\).
Given that the point \(F\) is the focus of the parabola \(C\),
- find the area, in terms of \(a\), of the triangle \(F X D\), giving your answer in its simplest form.