The normal at the point $P\left(a{p}^2,2ap\right)$ meets the parabola $y^2=4ax$ again at $Q\left(a{q}^2,2aq\right)$such that the lines joining the origin to $P$and $Q$are at right angle. Then, $p^2=$

The normal at  $\left(a{p}^2,2ap\right)$ to $y^2=4ax$ meets the parabola at $\left(a{q}^2,2aq\right)$ then

. $q=-p-\frac{2}{p}$                    ..(i)

Now, $OP\perp OQ$

$\begin{array}{l}\Rightarrow \frac{2ap-0}{a{p}^2-0}\times \frac{2aq-0}{a{q}^2-0}=-1\\ \Rightarrow pq=-4\end{array}$

$\Rightarrow p\left(-p-\frac{2}{p}\right)=-4$                      [Using (i)]

$\Rightarrow p^2=2$.