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.