- The normal to the parabola \(y ^ { 2 } = 4 a x\) at the point \(P \left( a p ^ { 2 } , 2 a p \right)\) passes through the parabola again at the point \(Q \left( a q ^ { 2 } , 2 a q \right)\).
The line \(O P\) is perpendicular to the line \(O Q\), where \(O\) is the origin.
Prove that \(p ^ { 2 } = 2\)