Let P(h, k) be a point in the plane of y2 = 4ax. It is known that the normal to parabola at (at2, 2at) is tx + y = 2at + at3. This normal passes through P(h,k
th + k = 2at + 2at + at3
at3 + (2a - h)t - k = 0 .....(1)
Equation (1) is a cubic equation in t and hence, in general, it has three roots and hence, there are three points on the curve at which normals drawn to the parabola are concurrent at P(h, k).
