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MathGroup Archive 2005

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Re: Circle equation problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61640] Re: Circle equation problem
  • From: "Valeri Astanoff" <astanoff at yahoo.fr>
  • Date: Mon, 24 Oct 2005 21:06:58 -0400 (EDT)
  • References: <dja2c3$fig$1@smc.vnet.net><djcgsv$6ka$1@smc.vnet.net> <djfmel$amv$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Daniele,

You're right.
One has to use SolveAlways instead of Solve :


In[1]:=
eq=Abs[p] == Abs[(G - X + I*Y)/(-1 + G*(X + I*Y))];
e1 = List@@eq ;
e2 = ComplexExpand[e1,{p,G}] ;
e3 = e2 ^2;
e4 = e3[[1]]-e3[[2]];
e5 = Numerator[e4//Together] ;
cir = (X-XCenter)^2+(Y-YCenter)^2-ray^2 ;
ce = CoefficientList[e5,{X,Y}]//Flatten;
cc = CoefficientList[cir,{X,Y}]//Flatten;
sol = SolveAlways[Thread[ce == cc],{X,Y}];

In[2]:=
{ray, XCenter, YCenter} /. sol /. G -> (.7 - .25 I) /. p -> (.8 + .9I)

Out[2]=
{{-0.45675, 0.315, -0.424365},
 {-0.45675, 0.315, 0.424365},
 {0.45675, 0.315, -0.424365}, 
 {0.45675, 0.315, 0.424365}}


hth

v.a.


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