conic sections


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conic sections

conic sections

(kon -ik) (conics) A family of curves that are the locus of a point that moves so that its distance from a fixed point (the focus) is a constant fraction of its distance from a fixed line (the directrix). The fraction, e , is the eccentricity of the conic. The value of the eccentricity determines the form of the conic. If e is less than 1 the conic is an ellipse. A circle is a special case of this with e = 0. If e = 1 the conic is a parabola and if e exceeds 1 the conic is a hyperbola.

These curves are known as conic sections because they can be obtained by taking sections of a right circular cone at different angles: a horizontal section gives a circle, an inclined one an ellipse, one parallel to the slope of the cone is a parabola, and one with an even greater inclination is a hyperbola (see illustration). Conics are important in astronomy since they represent the paths of bodies that move in a gravitational field. See also orbit.

Collins Dictionary of Astronomy © Market House Books Ltd, 2006

Conic sections

Circle, ellipse, parabola, and hyperbola; all produced by cutting a plane through a cone at different angles.
Illustrated Dictionary of Architecture Copyright © 2012, 2002, 1998 by The McGraw-Hill Companies, Inc. All rights reserved
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Although we can calculate the next term [[phi].sub.m+2] directly, the conic sections allow us to easily "track" the movements of the points from [mathematical expression not reproducible].
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At twelve years of age Pascal discovered Euclid's axioms unaided; at sixteen he wrote a treatise on conic sections, and at eighteen he invented a calculating machine.
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After reviewing prerequisites, the chapters consider such topics as equations and graphs, exponential and logarithmic functions, matrices and determinants, conic sections, and probability and statistics.
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Problems from Murray Klamkin; the Canadian collection

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