On detecting a wavefront described by 2D eikonal equation, when velocity in a medium depends on one spatial variable

In this paper, a 2D eikonal equation $f_x^2+f_y^2=(ky+b)^{2\alpha}$ is considered. If its solution is found, then the relation $f(x,y)=C$ determines the location of a wavefront. However, finding such solutions is still an open question. In this paper, we propose to directly find a curve in the parametric form, corresponding to the wavefront, without solving the equation as it is.