  We analyze existence, stability, and symmetry of point vortex relative
equilibria with one dominant vortex and N vortices with infinitesimal
circulation. The dimension of the problem can be reduced by taking an
infinitesimal circulation limit, resulting in the so-called (1+N)-vortex
problem. In this work, we first generalize the reduction to allow for
circulations of varying signs and weights. We then prove that symmetric
configurations require equality of two circulation parameters in the
(1+3)-vortex problem and show that there are stable asymmetric relative
equilibria. In a number of examples, we use rigorous methods from algebraic
geometry to count all relative equilibria.
