In our paper we approximate a set of given points by a general circle. More precisely, we consider the problem of locating and scaling the unit ball of some given norm k1 with respect to xed points on the plane such that the sum of weighted distances between the circle and the xed points is minimized, where the distance is measured by a norm k2. We present results for the general case. In the case that k1 and k2 are both block norms, we are able to identify a nite dominating set in R3 for the problem, which can be obtained as the intersection of cones.