Development of acoustic source localization techniques in anisotropic plates has gained attention in the recent past and still has scope of improvement. Most of such techniques existing in the literature either require known material properties or assume a straight line propagation of wave energy from the acoustic source to a sensor. These limitations have been overcome in recent years by employing wave front shape-based techniques. However, the existing wave front shape-based techniques are applicable in situations where the orientation of the axes of symmetry of the anisotropic plate is known beforehand. In the present study, a modified version of these techniques, namely, elliptical and parametric curve-based techniques, is proposed. This new version is useful when the angle between the axes of symmetry and the reference Cartesian coordinate system is unknown. In the new definition of the objective function, the orientation of the axes of symmetry of the anisotropic plate is treated as an input in the objective function in addition to the other unknowns like the source coordinates and the curve parameters. A numerical study illustrates how the modified new techniques can localize the acoustic source with sufficient accuracy in an anisotropic plate with unknown orientation of the axes of symmetry and its material properties.