2.19. The Conic Sections

A right circular cone can be generated by rotating a generator line G about an axis A with which it intersects at an angle 0<θ< π 4  at the vertex P.   Each of the upper and lower portions is called a nappe of the cone.  The curves obtained by the intersection of a plane with the surface of the cone are called conic sections or simply conics.  Depending on the angle of the plane, one can obtain 3 types of curves [see Fig.2.9].  With the help of the icecream-cone proof [see text], they can be identified with the parabola, ellipse and hyperbola defined in Fig.2.10.