a) The normals to the parabola x^2 = 4ay at the points P(2ap, ap^2) and Q(2aq, aq^2) are perpendicular to each other and meet at R. Prove that R lies on the parabola x^2 = a(y-3a)

b) P is a variable point on the parabola x^2=4ay and N is the foot of the perpendicular drawn from the focus S to the normal at P. Show that the locus of N is x^2 = a(y-a)

if anyone could help me with these problems, i would REALLY appreciate it, thankYOU !