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From: bs@faron.UUCP (Robert D. Silverman)
Newsgroups: net.math
Subject: Re: moRe: Conic sections (new problem)
Message-ID: <459@faron.UUCP>
Date: Sat, 1-Feb-86 19:54:40 EST
Article-I.D.: faron.459
Posted: Sat Feb  1 19:54:40 1986
Date-Received: Mon, 3-Feb-86 04:49:04 EST
References: <1165@homxb.UUCP> <557@well.UUCP> <532@well.UUCP> <11591@ucbvax.BERKELEY.EDU> <660@eagle.ukc.ac.uk>
Organization: The MITRE Coporation, Bedford, MA
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> Keywords:
> Xpath: ukc eagle
> 
> Having seen half a dozen replies to the original posting, all giving
> information I found in Analytical Geometry textbooks going back 150 years, I
> thought I'd try a slight change of direction. So:
> 
> Does anyone know (or know where to find) expressions for the coefficients of
> the (oft quoted) general second order equation in terms of the radii
> ($r_{major},r_{minor}$), center ($x_c,y_c$) and rotation ($theta$) of a
> circle or ellipse (I'm not interested in the other conics). I've
> found/discovered/guessed the forms with center and radii, but when I
> try to add rotation, I'm stumped.
> 
> I'd tell you why I'm interested in this, but given the recent flames about
> what should (or shouldn't) be in this group, I don't think you'd want to
> know.
> 
> 	Ian Utting	iau@ukc.uucp
> (From the above, you'll have guessed that I'm no mathematician).

One removes the linear terms in x any y by translation: completing the
square allows one to transform x' = x + a  and y' = y + b. To rotate
by an angle theta add a Bxy term where

	tan(2 theta) = B/(A-C)

Bob Silverman