If this disease is genetic--what are the possible genotypes of the parents?

The parents must either be Xx,Xx (both parents are carriers), xx,Xx (one of the parents has the disease, the other is a carrier), or xx,xx (both of the parents have the disease). If the parents are XX,Xx then there is a chance their children might be carriers, but none of them will have it. If the parents are XX,XX then the mutated gene isn't present in the family at all.