$\text{ If the three normal drawn to the parabola, }{y}^2=2x\text{ pass through the point }(a,0)a\ne 0,\text{ then ' }a\text{ ' }$$\text{must be greater than}$:

$\begin{array}{l}\text{Equation of normal to the parabola }{y}^2=4ax\text{\hspace{0.17em} at }t\text{\hspace{0.17em} is }y+xt=2at+a{t}^3\\ \text{Here }a=\frac{1}{2},\text{\hspace{0.17em}So the equation of the normal is }y+xt=t+\frac{t^3}{2}\\ \text{It is passing through the point }\left(a,0\right)\text{\hspace{0.17em}and }t\text{\hspace{0.17em} has three values. }\end{array}$

                                  $\begin{array}{c}0+at=t+\frac{t^3}{2}\\ t^3=2at-2t\\ =2t\left(a-1\right)\\ t^2=2\left(a-1\right)\\ a-1>0\\ a>1\end{array}$