This lecture covers the concept of points at infinity in a plane section of a circular cone, discussing the existence of such points and their relationship with generatrices. It also explores different cases for conic sections, including ellipses, parabolas, and hyperbolas, based on the intersection of tangents. The construction of asymptotes for conic sections is detailed, along with the determination of the direction of axes and vertices. The lecture concludes with the analysis of tangents and asymptotes in hyperbolic sections of circular cones.