If a circcle passes through the point $(a, b)$ and cuts the circle $x^2 + y^2 = p^2$ orthogonally, then the equation of the locus of its centre is :

Question

( A ) $x^2 + y^2 - 2ax - 3by + (a^2 - b^2 - p^2) = 0$
( B ) $x^2 + y^2 - 3ax - 4by + (a^2 b^2 - p^2) = 0$
( C ) $2ax + 2by - (a^2 + b^2 + p^2) = 0$
( D ) $2ax + 2by - (a^2 - b^2 + p^2) = 0$