A family of circles can be constructed as ##x^2 + y^2 + {f_1}x + {g_1}y + h_1 + k(x^2 + y^2 + {f_2}x + {g_2}y + h_2) = 0##.

By altering the k, an infinitely number of circles through those two points are obtained. So is any circle existed that it cannot be obtained by the family of circles?