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Re: Ellipse equation simplification on Mathematica:

• To: mathgroup at smc.vnet.net
• Subject: [mg77044] Re: Ellipse equation simplification on Mathematica:
• From: Narasimham <mathma18 at hotmail.com>
• Date: Fri, 1 Jun 2007 02:47:26 -0400 (EDT)
• References: <f2emof$35h$1@smc.vnet.net><200705300929.FAA13381@smc.vnet.net>

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> >>>>> On May 19, 1:54 pm, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote:
> >>>>>> On 18 May 2007, at 19:06, 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 = 0
----
For case of cp= -1,when the tube is rotated by ph = 180 deg and moved
horizontally,the taut threads cross each other in bow-tie/butterfly
mode.The locus is an ellipse as simplification gives effective a and c
simple relations.

aEff = (a-d) and cEff = (c-d).

Narasimham