Hello, everybody. I need help...
Show that, for all values of p, the point P given by x=ap2, y=2ap lies on the curve y2=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 (aq2, 2aq). Show that p2+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 y2(x+2a) +4a3=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 y2(x+2a) +4a3=0” in Q (b). Can somebody help me?