- The parabola \(C\) has equation \(y ^ { 2 } = \frac { 4 } { 3 } x\)
The point \(P \left( \frac { 1 } { 3 } t ^ { 2 } , \frac { 2 } { 3 } t \right)\), where \(t \neq 0\), lies on \(C\).
- Use calculus to show that the normal to \(C\) at \(P\) has equation
$$3 t x + 3 y = t ^ { 3 } + 2 t$$
The normal to \(C\) at the point where \(t = 9\) meets \(C\) again at the point \(Q\).
- Determine the exact coordinates of \(Q\).