The number of points on $y^2=4ax$ at which the normal chords drawn subtend a right angle at the vertex 

Let $P\left(a{t}^2,2at\right)$ be  a point on the parabola  

$y^2=4ax$  If the normal chord at P subtends a right angle at the

vertex, then 

 $t^2=2\Rightarrow t=\pm \sqrt{2}$

Thus, there are two points on the parabola.