- The parabola \(C\) has equation \(y ^ { 2 } = 4 a x\) where \(a\) is a positive constant.
The point \(P \left( a t ^ { 2 } , 2 a t \right) , t \neq 0\), lies on \(C\)
The normal to \(C\) at \(P\) is parallel to the line with equation \(y = 2 x\)
- For the point \(P\), show that \(t = - 2\)
The normal to \(C\) at \(P\) intersects \(C\) again when \(x = 9\)
- Determine the value of \(a\), giving a reason for your answer.