Due to the Mizarians' traditions of peace, the planet was conquered six times in a matter of three centuries. (TNG: "Allegiance")
According to the Star Trek: Star Charts (pg. 44, "United Federation of Planets III"), the Mizar system was located in the Beta Quadrant. This system, also known as Zeta Ursae Majoris, was a five star system. Primary was a Class A star with a magnitude of +3, which was ten times brighter than Sol. The secondary, tertiary, quarternary, and quinary were Class A stars. In the mid-22nd century, this system was in non-aligned space. In the late 24th century, this system was in or near Federation space.