In this article, the planes meeting a non-singular quadric of PG\((4,q)\) in a conic are characterized by their intersection properties with points, lines and \(3\)-spaces.
Citation
Stefano Innamorati, Mauro Zannetti. A Characterization of the Planes Secant to a Non-Singular Quadric in PG\((4,q)\)[J], Ars Combinatoria, Volume 102. 435-445. .