Vulpe, Nicolae2025-07-032024VULPE, Nicolae. The Family of Quadratic Systems with Two Invariant Conics: Parabola and Hyperbola. In: International Conference dedicated to the 60th anniversary of the foundation of Vladimir Andrunachievici Institute of Mathematics and Computer Science, MSU, October 10-13 2024. Chisinau: [S. n.], 2024, pp. 212-217. ISBN 978-9975-68-515-3.978-9975-68-515-3https://msuir.usm.md/handle/123456789/18258We consider the family of quadratic systems QSPHη>0 having three real distinct infinite singularities and possessing at least two invariant conics: a parabola and a hyperbola. All the possible configurations of these invariant conics including invariant lines (when they exist) are determined. We describe completely the set of such systems and we prove the existence of exactly 38 distinct configurations which could possess a system in this family.enquadratic systemsinvariant conicsinvariant lineconfigurations of invariant conicsaffine transformationArticle