Let (x, y) be any point on the parabola y2 = 4x. Let P be the point that divides the line segment from (0,0) to (x, y) in the ratio 2:3. Then locus of P is
x2=y
5y2=2x
5y2=8x
5x2=2y
Let P be (h, k)
then h=2x5, k=2y5
As (x, y) lies on the parabola y2=4x
5k22=45h2
⇒ 5k2=8h
⇒Locus of P is 5y2=8x.