If a circle passes through the points $(a,b)$ and cuts the circle $x^2+y^2=4$ orthogonally, then the locus of its centre is

Question

$\begin{array}{1 1}(A)\;2ax-2by-(a^2+b^2+4)=0 \\(B)\;2ax-2by-(a^2+b^2+4)=0 \\(C)\;2ax-2by+(a^2+b^2+4)=0 \\(D)\;2ax+2by+(a^2+b^2+4)=0 \end{array}$