2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57416In this work, we study the Lie-point symmetries of Kepler--Ermakov systems presented by C. Athorne in J. Phys. A24 (1991), L1385--L1389. We determine the forms of arbitrary function H(x,y) in order to find the members of this class possessing the sl(2,R) symmetry and a Lagrangian. We show that these systems are usual Ermakov systems with the frequency function depending on the dynamical variables.arxiv version is already officialMathematical Physicstext