Eukaryotic enzymes of the DNA TOPOISOMERASES, TYPE II class that catalyze ATP-dependent breakage of both strands of DNA, passage of the unbroken strands through the breaks, and rejoining of the broken strands. These enzymes bring about relaxation of the supercoiled DNA and resolution of a knotted circular DNA duplex. Isozymes of the eukaryotic DNA topoisomerase II consist of homodimers of alpha or beta subunits.