AHSME 1960 Problem 12

The locus of the centers of all circles of given radius $a$, in the same plane, passing through a fixed point, is: $\textbf{(A) }\text{a point} \textbf{(B) }\text{a straight line} \textbf{(C) }\text{two straight lines} \textbf{(D) }\text{a circle} \textbf{(E) }\text{two circles}$