8. The parabola \(C\) has equation \(y ^ { 2 } = 48 x\).
The point \(P \left( 12 t ^ { 2 } , 24 t \right)\) is a general point on \(C\).
- Find the equation of the directrix of \(C\).
- Show that the equation of the tangent to \(C\) at \(P \left( 12 t ^ { 2 } , 24 t \right)\) is
$$x - t y + 12 t ^ { 2 } = 0$$
The tangent to \(C\) at the point \(( 3,12 )\) meets the directrix of \(C\) at the point \(X\).
- Find the coordinates of \(X\).