The Syzygetic Pencil of Cubics

All order cubics through any given eight points have a ninth point in common and constitute a pencil determined by any two cubics through the eight points. It is known that a cubic and its Hessian intersect in the nine inflexional points of the cubic, which are also the inflexional points of the Hessian. The pencil determined by these two cubics is called a syzygetic pencil.