# 3 normals to a parabola

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.

• – lab bhattacharjee May 5 '17 at 16:39
• Ty very much 4 this link #lab bhattacharjee – palash jain May 5 '17 at 16:48

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).