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MathGroup Archive 2007

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Re: Re: Ellipse equation simplification on Mathematica:

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77075] Re: [mg77032] Re: Ellipse equation simplification on Mathematica:
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 2 Jun 2007 04:24:59 -0400 (EDT)
  • References: <f2emof$35h$1@smc.vnet.net><200705300929.FAA13381@smc.vnet.net> <200706010641.CAA25336@smc.vnet.net>

This can't be true without some additional assumptions, since, as I  
showed in my reply:

  Expand[(-y^2)*(a - d)^2 + (a^2 - 2*d*a - c*(c + 2*cp*d))*(a - d)^2 +
          (-a^2 + 2*d*a + c^2 + (cp^2 - 1)*d^2 + 2*c*cp*d)*x^2 == 0 /.
      {a -> 181, c -> -(39/10), d -> 100, cp -> 1}]

(267421*x^2)/100 - 6561*y^2 - 1754549181/100 == 0


which is a hyperbola. However, in this case the original equations  
have no solutions.

Andrzej Kozlowski


On 1 Jun 2007, at 15:41, Narasimham wrote:

> On May 31, 12:19 pm, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote:
>> On 30 May 2007, at 18:29, Narasimham wrote:
>
>> (-y^2)*(a - d)^2 + (a^2 - 2*d*a - c*(c + 2*cp*d))*(a - d)^2 +
>> (-a^2 + 2*d*a + c^2 + (cp^2 - 1)*d^2 + 2*c*cp*d)*x^2
>
> The above can be simplified, and they are shown capable of being cast
> into canonical form of ellipses :
>
> (x/aEff)^2 + y^2/(aEff^2 - cEff^2) = 1
>
> For case x-axis parallel tube cp = 1, forming trapeziums at each
> stage:
>
> aEff = (a - d), cEff = (c + d).
>
> For case x-axis perpendicular to tube cp = 0:
>
> aEff = (a - d) V, cEff = c V
>
> where V = Sqrt((a^2 -2 a d -c^2)/(a^2 -2 a d -c^2 + d^2) )
>
> Narasimham
>
>



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