Langara College - Department of Mathematics and Statistics

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Internet Resources for the Calculus Student - Topics in Precalculus

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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,

please do let
us know and we will add them here.