This article considers the path tracking problem for underactuated ships with general form of dynamics including uncertainties. By introducing certain two polar coordinate transformations, the ship's tracking kinematics and dynamics can be transformed into certain two-inputs-two-outputs nonlinear strict-feedback form. To avoid possible singularity problem in the backstepping control design, we introduce an asymptotic modification of orientation concept. Presented tracking scheme can guarantee the uniformly ultimately boundedness of closed-loop system in terms of polar coordinates. For the convenience of comparison with previous related works, where all tracking schemes were discussed in the Cartesian frame, we carry out some case studies to investigate the conditions under which the proposed tracking method can guarantee the same stability and convergence properties of tracking errors in the Cartesian frame. Numerical simulation studies are also carried out to demonstrate the effectiveness of presented tracking scheme.