College Algebra, 4th Edition

Section 7.1 Conic Sections: Overview

Most of the sections in this chapter focus on the plane curves called conics or conic sections. As the name implies, these curves are the sections of a cone (similar to an ice cream cone) formed when a plane intersects the cone.

Euclid defined a cone as a surface generated by rotating a right triangle about one of its legs. However, the following description of a cone given by Apollonius is more appropriate.

Right Circular Cone

Draw a circle on a plane (say, horizontal). Draw a line l, called the axis, passing through the center of the circle and perpendicular to the plane. Choose a point V above the plane ...