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MathGroup Archive 2007

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Re: Ellipse equation simplification on Mathematica:

  • To: mathgroup at smc.vnet.net
  • Subject: [mg76234] Re: Ellipse equation simplification on Mathematica:
  • From: CKWong <CKWong.P at gmail.com>
  • Date: Fri, 18 May 2007 06:12:21 -0400 (EDT)
  • References: <f2emof$35h$1@smc.vnet.net>

As far as proving it to be an ellipse is concerned, your equation
describes the projection onto the x-y plane of an ellipse with foci at
Cartesian coordinates
   { -dcp cth - c, -d cp sth, -d sth }  and  { dcp cth + c, d cp sth,
d sth }
Since the shadow of an ellipse is an ellipse, QED.

Parametrization can be easily (I hope) worked out for the 3-D ellipse
& then projected onto the x-y plane.  Good luck.



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