Let \(A\) be the point \((0,4)\) and \(B\) be a moving point on \(x\)-axis. Let \(M\) be the midpoint of \(A B\) and let the perpendicular bisector of \(A B\) meets the \(y\)-axis at \(R\). The locus of the midpoint \(P\) of \(M R\) is
(A) \(y+x^{2}=2\)
(B) \(x^{2}+(y-2)^{2}=\frac{1}{4}\)
(C) \((y-2)^{2}-x^{2}=\frac{1}{4}\)
(D) \(x^{2}+y^{2}=16\)
Ans(A)