  In this paper, we study the existence and qualitative properties of positive
solutions to a Choquard-type equation with Hardy potential. We develop a
nonlocal version of concentration-compactness principle involving the Hardy
potential to study the existence and the asymptotic behavior of positive
solutions by transforming the original problem into a new nonlocal problem in
the weighted Sobolev space. Moreover, we obtain the symmetry of solutions by
using the moving plane method.
