Question 8 - A-Level Maths

The point \(P \left( 2 p ^ { 2 } , 4 p \right)\) lies on the parabola with equation \(y ^ { 2 } = 8 x\)
1. Show that the point \(Q \left( \frac { 2 } { p ^ { 2 } } , \frac { - 4 } { p } \right)\), where \(p \neq 0\), lies on the parabola.
2. Show that the chord \(P Q\) passes through the focus of the parabola.
The tangent to the parabola at \(P\) and the tangent to the parabola at \(Q\) meet at the point \(R\)
Determine, in simplest form, the coordinates of \(R\)