Find the equation of the normal to the parabola \(y^2=4ax\) at the point \((at^2,2at)\).

Prove that, if \(p^2>8\), two chords can be drawn through the point \((ap^2,2ap)\) which are normal to the parabola at their second points of intersection, and that the line joining these points of intersection meets the axis of the parabola in a fixed point, independent of \(p\).