A quadric cone

This figure shows a finite portion of a quadric cone. The quadric cone is the simplest quadric ruled surface, i.e., it is a surface of degree 2 that contains infinitely many lines. In fact, the vertex of the cone is at the origin, and every line that connects the origin to a point of the surface lies on the cone.

In this version, cross sections perpendicular to the axis of the cone are circles, and the equation has the following form:

z² = a²(x² + y²),

where a is a nonzero real number. This figure was drawn with the value a = 2.
Click here to go:

back to the main drawing of the hyperboloid of one sheet
to a drawing that shows the rulings on a hyperbolic paraboloid

I made the figure on this page by substituting my own data in a Geometry Center webpage.

Prof. Joel Roberts
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
USA

Office: 351 Vincent Hall
Phone: (612) 625-1076
Dept. FAX: (612) 626-2017
e-mail: roberts@math.umn.edu
http://www.math.umn.edu/~roberts