8 The parametric equations of a curve are \(x = 2 t ^ { 2 } , y = 4 t\). Two points on the curve are \(P \left( 2 p ^ { 2 } , 4 p \right)\) and \(Q \left( 2 q ^ { 2 } , 4 q \right)\).
- Show that the gradient of the normal to the curve at \(P\) is \(- p\).
- Show that the gradient of the chord joining the points \(P\) and \(Q\) is \(\frac { 2 } { p + q }\).
- The chord \(P Q\) is the normal to the curve at \(P\). Show that \(p ^ { 2 } + p q + 2 = 0\).
- The normal at the point \(R ( 8,8 )\) meets the curve again at \(S\). The normal at \(S\) meets the curve again at \(T\). Find the coordinates of \(T\).