  In this present paper, we study the splitting of nodal plane curves with
respect to contact conics. We define the notion of splitting type of such
curves and show that it can be used as an invariant to distinguish the embedded
topology of plane curves. We also give a criterion to determine the splitting
type in terms of the configuration of the nodes and tangent points. As an
application, we construct sextics and contact conics with prescribed splitting
types, which give rise to new Zariski-triples.
