Let \(\Gamma\) be an algebraic curve in \(\mathbb{P}^{2}\). A smooth conic \(\Delta\subset\mathbb{P}^{2}\) is called a contact conic of \(\Gamma\) if all of the intersection points of \(\Gamma\) and \(\Delta\) are smooth points of \(\Gamma\) and for them the intersection multiplicity \(I_{P}(\Gamma,\Delta)\geq2\). \(\Gamma\) with even (means intersection multiplicities are even) contact conic \(\Delta\) is a splitting curve of type \((m,n),\) \(m\leq n,\) with respect to \(\Delta\) if for the double cover \(\pi_{\Delta}:X_{\Delta}\rightarrow \mathbb{P}^{2}\) branched along \(\Delta\) the pullback \(\pi_{\Delta}^{\ast}\Gamma=D^{+}+D^{-}\) for an \((m,n)\) divisor \(D^{+}\) on \(X_{\Delta} \cong\mathbb{P}^{1}\times\mathbb{P}^{1}\), where \(D^{-}\) is \(D^{+} \) after the covering transformation of \(X_{\Delta}.\) The main theorem is a criterion for determining the splitting type of a nodal curve \(\Gamma\) (means singular points of \(\Gamma\) are nodes) with respect to an even contact conic in terms of the configuration of the nodes and tangent points of \(\Gamma\) and \(\Delta\). The authors apply the results to Zariski pairs of curves.