CALCULUS Understanding Its Concepts and Methods

Conic section, Ellipse, Hyperbola, Parabola

A conic section is a curve whose points
satisfy an equation of the form
*Ax*^{2} + *Bxy* + *Cy*^{2} +
*Dx* + *Ey* + *F* = 0. The
type of curve determined by the general form depends on the sign of the
discriminant, where the
discriminant is the
number
If
,
the general form of the quadratic equation
determines(a
circle being considered as a special case of an ellipse) or the equation has
purely imaginary solutions. The degenerate cases give a *pair of
intersecting lines*, a *line*, or a *point*.

From a geometric point of view, a conic section is the intersection of a cone with a plane:

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.