  We provide a tool how one can view a polynomial on the affine plane of
bidegree $(a,b)$ - by which we mean that its Newton polygon lies in the
triangle spanned by $(a,0)$, $(0,b)$ and the origin - as a curve in a
Hirzebruch surface having nice geometric properties. As an application, we
study maximal $A_k$-singularities of curves of bidegree $(3,b)$ and find the
answer for $b\leq 12$.
