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 1:3. Then the locus of P is

Let the coordinates of P, whose locus is to be determined, be (h,k). Since this point divides the line joining (0,0) to (x,y) in the ratio 1:3. So coordinates of point P will be (x/4, y/4). So, h=x/4 and k=y/4. Or, x=4h, and y=4k. Since, y²=4x ⇒(4k)²=4(4h) ⇒16k²=16h ⇒k²=h Or y²=x, which is the locus of P.