cbicon.png CALCULUS Understanding Its Concepts and Methods

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Conic section, Ellipse, Hyperbola, Parabola

A conic section is a curve whose points satisfy an equation of the form Ax2 + Bxy + Cy2 + 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 MATHIf MATH, the general form of the quadratic equation determinesMATH(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:


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


Cone

Ellipse

Hyperbola

Parabola

Quadric surfaces


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.

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