3. A parabola \(C\) has cartesian equation \(y ^ { 2 } = 16 x\). The point \(P \left( 4 t ^ { 2 } , 8 t \right)\) is a general point on \(C\).
- Write down the coordinates of the focus \(F\) and the equation of the directrix of \(C\).
- Show that the equation of the normal to \(C\) at \(P\) is \(y + t x = 8 t + 4 t ^ { 3 }\).