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A **conic** (or **conic section**) is a plane curve that can be
obtained by intersecting a cone (Section 13.3) with a plane
that does not go through the vertex of the cone. There are three
possibilities, depending on the relative position of the cone and the
plane (Figure 1). If no line of the cone is parallel to
the plane, the intersection is a closed curve, called an **ellipse**.
If one line of the cone is parallel to the plane, the intersection is
an open curve whose two ends are asymptotically parallel; this is
called a **parabola**. Finally, there may be two lines in the cone
parallel to the plane; the curve in this case has two open pieces,
and is called a **hyperbola**.

**Figure 1:** Left: A section of a cone by a plane can yield an ellipse
(left), a parabola (middle) or a hyperbola (right).

- 7.1 Alternative Characterization
- 7.2 The General Quadratic Equation
- 7.3 Additional Properties of Ellipses
- 7.4 Additional Properties of Hyperbolas
- 7.5 Additional Properties of Parabolas

*Silvio Levy
Wed Oct 4 16:41:25 PDT 1995*

This document is excerpted from the 30th Edition of the *CRC Standard Mathematical Tables and Formulas* (CRC Press). Unauthorized duplication is forbidden.