Show that the equation of the normal to the parabola $\displaystyle y^2=ax$ at the point $\displaystyle (at^2, 2at0$ is $\displaystyle y+tx=2at+at^3$.

If this normal meets the curve again at the point $\displaystyle (aT^2,2aT)$ show that

$\displaystyle t^2+tT+2=0$

and deduce that $\displaystyle T^2$ is greater than 8.

My problem here is deducing the $\displaystyle T^2$ is greater than 8.

Thanks