3 normals to a parabola

Question

What is the least value of $z$ such that 3 normals from $P(z,0)$ can be drawn to $y^2=4ax$?

I thought that any point inside the parabola should satisfy this condition but I was proven wrong.

Answer 1

Hint...write down the equation of the normal at $(at^2,2at)$ and plug in $x=z,y=0$

The resulting equation in $t$ must have three distinct roots (one of which is zero).