For a given holonomic system of two degrees of freedom and for a given monoparametric family of trajectories (not necessarily isoenergetic), generated by the known potential of the system, we find a formula offering the Riemannian curvature associated with the Maupertuis metric. In the light of the inverse problem of dynamics, we introduce also the notion of the family zero-curvature curves (FZCC). As an application, we derive the pertinent formulae for all members of a family of concentric circular orbits produced by the appropriate potentials, we examine the connection of their stability to the sign of the curvature and we compare with stability deduced by other considerations, including numerical integration.