Abstract
This chapter discusses linear systems of quadrics. It also discusses Pencil of quadrics, Self-polar tetrahedron of a pencil of quadrics, and contact of quadrics. An arbitrary plane cuts the quadrics F and F′ in conies that have four common points. Consequently, F + kF′ = 0 represents a system of quadrics, called a pencil of quadrics, passing through a space curve of the fourth order, called the base curve. Through any point, not on the base curve, there passes one and only one quadric of the pencil because is linear in k. If the base curve has a double point with distinct tangents, the quadrics of the pencil all touch these two tangent lines and so have a common tangent plane at the double point. Any two quadrics of the pencil are said to have single contact with one another.
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