Show that the equation of the normal to the parabola at the point is .
If this normal meets the curve again at the point show that
and deduce that is greater than 8.
My problem here is deducing the is greater than 8.
Well since you've deduced it is easy to show that is greater than 8. Since the normal intersects the parabola in 2 points, the discriminant of the equation in t has to be greater than zero (for a tangent, discriminant = 0, discriminant is denoted by delta). Therefore, we get