For which orbit is the total mechanical energy of the cosmic body negative, for which is zero and for which is positive?

For a body in an elliptical orbit, the total mechanical energy is less than zero in a parabolic orbit equal to zero, in a hyperbolic orbit it is greater than zero. Equality to zero of mechanical energy means equality to zero at infinity of both kinetic and potential energies. A body in a hyperbolic orbit even at infinity has a nonzero velocity.