  In this paper we generalize some results by Siersma, Pellikaan, and de Jong
regarding morsifications of singular hypersurfaces whose singular locus is a
smooth curve, and present some applications to the study of Yomdin-type
isolated singularities. In order to prove these results, we discuss the
transversal discriminant of such singularities and how it relates to other
algebraic and topological invariants.
