Using homogeneous coordinates, cross product, determinants, and MATLAB the authors prove the well-known Pascal hexagon theorem and its converse. In the same way they confirm simple propositions on conics and Theorem 6.13 from [R. Bix, Conics and cubics. A concrete introduction to algebraic curves. 2nd ed. New York, NY: Springer (2006; Zbl 1106.14014)] which deals with eight conic points and the eight intersection points of certain mutual joins of the given eight points. For this “eight point theorem” the authors present a second proof which avoids the computational brute force approach.