Formulas for setting a location of the wavefront propagating in a medium with power dependence of velocity on a coordinate

In this paper, the 2D eikonal equation $f_x^2+f_y^2=(ky)^{2\alpha}$ is considered. If $f$ is its solution, the relation $f(x,y)=C$ sets the wavefront location. However, obtaining solutions is associated with some difficulties. In this paper, the author develops the earlier proposed technique that enables the detection of a parametric curve to set the wavefront without solving the above equation.