Overview

A conic section, as the name suggests, is a section taken through a cone. At the intersection of the sectional plane and the surface of the cone, curves having many different shapes are produced, depending on the inclination of the plane, and it is these curves which are referred to generally as conic sections. Although the origin of conic sections lies in solid geometry, the properties are readily expressed in terms of plane geometrical curves. In Fig. B.1a, a reference line for conic sections, known as the directrix, is shown as Z-D. The axis for the conic sections is shown as line Z-Z ?. The axis is perpendicular to the directrix. The point S on the axis is called the focus. For all conic sections, the focus has the particular property that the ratio of the distance SP to distance PQ is a constant. SP is the distance from the focus to any point P on the curve (conic section), and PQ is the distance, parallel to the axis, from point P to the directrix. The constant ratio is called the eccentricity, usually denoted by e. Referring to Fig. B.1a,

Figure B.1

(B.1)

The conic sections are given particular names according to the value of e, as shown in the following table: