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From: lotto@brahms.BERKELEY.EDU (Ben Lotto)
Newsgroups: net.math
Subject: Re: Question came up at a party
Message-ID: <11517@ucbvax.BERKELEY.EDU>
Date: Thu, 23-Jan-86 15:53:36 EST
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Posted: Thu Jan 23 15:53:36 1986
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The general equation that includes all conics is

	a*x^2 + b*x*y + c*y^2 + d*x + e*y + f = 0

where if all of a, b, and c = 0 the graph degenerates into a line.  Here
are some cases:

	b=d=e=0, a,c>0:  Circle or ellipse
	b=d=e=0, a>0, c<0:  Hyperbola
	b=c=0:  Parabola

Varying the other coefficients will transform the graph by rotation,
translation, or dilation.

-Ben