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MathGroup Archive 2004

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Re: Solve bug?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52731] Re: [mg52705] Solve bug?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 11 Dec 2004 05:21:36 -0500 (EST)
  • References: <200412100123.UAA18967@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 10 Dec 2004, at 10:23, paul at selfreferral.com wrote:

> Solve seems to be returning an invalid answer when I do this:
>
> c1 = (-50 + x)^2 + (-50 + y)^2 == 156.25
> c2 = (-4.5 + x)^2 + (-56.25 + y)^2 == 156.25
>
> Solve[{c1,c2}]
> {{x -> 16, y -> 43.75}, {x -> 84, y -> 43.75}}
>
> This answer is so wrong!!??
> Those two points are completely off. Not even close.
>
> c1 and c2 are the equations of two overlapping circles.
> Use ImplicitPlot to verify this fact.
> Why can't Mathematica resolve this simple sytem of equations correctly?
>
> If I am doing something wrong please tell me what it is.
>
> Also how can I cut and paste text from a mathematica notebook without
> getting all the slashes?
> Your help is greatly appreciated.
>
> Regards,
> Paul
>


You are doing everything wrong.

1. Matheamtica 5.0 returns:


c1 = (-50 + x)^2 + (-50 + y)^2 == 156.25;


c2 = (-4.5 + x)^2 + (-56.25 + y)^2 == 156.25;


Solve[{c1, c2}]

{{x -> 27.25 - 2.6214539372377144*I, y -> 53.125 - 19.08418466309056*I},
   {x -> 27.25 + 2.6214539372377144*I, y -> 53.125 + 
19.08418466309056*I}}

Which means that there are no real solutions. And

2). You don't need ImplicitPlot.

gr1=ParametricPlot[{50+Sqrt[156.25]
       Cos[th],50+Sqrt[156.25] Sin[th]},{th,0,2Pi},
               AspectRatio->Automatic,DisplayFunction\[Rule]Identity];


gr2=ParametricPlot[{4.5+Sqrt[156.25]
       Cos[th],56.25+Sqrt[
               156.25] Sin[th]},{th,0,2Pi},AspectRatio\[Rule]Automatic,
               DisplayFunction->Identity];


Show[gr1,gr2,DisplayFunction->$DisplayFunction]


Shows that the circles obviously do not interest.

3. There is not need to do any of that at all. The centers of the 
circles are
{50,50} and {4.5,56.25}. The distance between the centers is:


Sqrt[({50, 50} - {4.5, 56.25}) . ({50, 50} - {4.5, 56.25})]


45.92725225832697

The sum of the radii (which are equal) is:

2*Sqrt[156.25]

25.

So since the distance between the centers is larger than the sum of the 
radii ....





Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/~andrzej/
http://www.mimuw.edu.pl/~akoz/


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