The problem of the optical radiation propagation through a medium with parabolic distribution of the imaginary part of dielectric constant has been solved analytically by the diffraction rays method in the paraxial approximation. It is shown that the diffraction rays method allows energy flow lines to be traced for the known arbitrary distribution of the dielectric constant of the medium taking into account the diffraction and refraction on an inhomogeneous absorption profile. The geometrical optics approximation for the given media is considered. It is found that the optical ray trajectory in the medium with inhomogeneous absorptance depends not only on the complex dielectric constant distribution, but also on the wavefront phase distribution. This means that the rays outgoing from one point of space in the same directions but belonging to wavefronts with different curvature radii in the vicinity of the given point will propagate along different trajectories. It is the fundamental difference between the geometric optics of homogeneously and inhomogeneously absorbing media.