  We show that the ground state interface geometry of binary condensates in the
phase separated regime undergoes a smooth transition from planar to ellipsoidal
to cylindrical geometry. This occurs for condensates with repulsive
interactions as the trapping potential is changed from prolate to oblate. The
correct ground state geometry emerges when the interface energy is included in
the energy minimization. Where as energy minimization based on Thomas-Fermi
approximation gives incorrect geometry.
