  We construct analytical initial data for a slowly moving and rotating black
hole for generic orientations of the linear momentum and the spin. We solve the
Hamiltonian constraint approximately and work out the properties of the
apparent horizon and show the dependence of its shape on the angle between the
spin and the linear momentum. In particular a dimple, whose location depends on
the mentioned angle, arises on the 2-sphere geometry of the apparent horizon.
We exclusively work in the case of conformally flat initial metrics.
