If P be the point (1, 0)  and Q, a point on the locus y2 = 8x. The locus of the mid point of PQ is:

Let the coordinates of Q be (2t2, 4t) coordinates of the mid point of PQ are2t2+12,2t Let h=2t2+12,k=2t Eliminating t, we get 4h=k2+2So the required locus is y2−4x+2=0