Let $A$ be the fixed point $(0,4)$ and $B$ be a moving point $(2t, 0)$. Let $M$ be the mid-point of $AB$ and let the perpendicular bisector of $AB$ meet the $y$-axis at $R$. The locus of the mid-point $P$ of $MR$ is\\
(A) $y + x ^ { 2 } = 2$\\
(B) $x ^ { 2 } + ( y - 2 ) ^ { 2 } = 1 / 4$\\
(C) $( y - 2 ) ^ { 2 } - x ^ { 2 } = 1 / 4$\\
(D) none of the above