Langara College - Department of Mathematics and Statistics

## Conic Sections

Conic Sections can be described geometrically as the curves that arise when a cone is sliced by a plane, or in other ways that don't at first seem to be the same but are in fact equivalent.

A nice animation of the slicing is provided as one of the 'MathCad Animations' at Old Dominion University in Virginia.

All of the conic sections can be described by quadratic equations. In the special case of a quadratic function equation, the graph is a parabola (this corresponds to the cutting plane being parallel to the side of the cone).

When the plane cuts more directly across the cone, the result is an ellipse (the circle is a special case of this), and when it is closer to being parallel to the axis of the (double) cone, the result is a hyperbola (and a special case of this is just two crossing straight lines - when the cutting plane actually includes the axis of the cone).

For more details and some exercises try the section on conics at the University of Saskatchewan's Exercises in Math Readiness site.

Various other interesting geometric properties of these curves and their equations are illustrated by applets and movies on the web.

If you have come across any good links to web-based material about conic sections,