Let O be the origin and A be a point on the curve $y^2=4x$. Then the locus of the mid point of OA is :

Question

\[\begin {array} {1 1} (a)\;x^2=4y & \quad (b)\;x^2=2y \\ (c)\;y^2=16 x & \quad (d)\;y^2=2x \end {array}\]