Hello, everybody. I need help...

Show that, for all values of p, the point P given by x=ap^{2}, y=2ap lies on the curve y^{2}=4ax.

a) Find the equation of this normal to this curve at the point P.

If this normal meets the curve again at the point Q (aq^{2}, 2aq). Show that p^{2}+pq+2=0

b) Determine the coordinates of R, the point of intersection of the tangents of the curve at the point P and Q.

Hence, show that the locus of the point R is y^{2}(x+2a) +4a^{3}=0

I already solved Q (a) and first question of Q (b). However, I can’t solve the last question: “Hence, show that the locus of the point R is y^{2}(x+2a) +4a^{3}=0” in Q (b). Can somebody help me?

Thanks!!