In a nutshell, a pencil of quadrics is a family of quadrics where all the elements intersect with the base curve. To build them, these steps are followed: 1) 2 Quadrics are chosen, 2) A linear combination is made, 3) The base curve is obtained, which is the intersection of the original quadrics, 4) The singular quadrics are identified, which is when the determinant of the linear combination is zero, 5) The pencil is graphed.
