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Ellipse equation simplification on Mathematica:

• To: mathgroup at smc.vnet.net
• Subject: [mg76147] Ellipse equation simplification on Mathematica:
• From: Narasimham <mathma18 at hotmail.com>
• Date: Wed, 16 May 2007 05:55:33 -0400 (EDT)

Reference is to:
http://groups.google.co.in/group/geometry.puzzles/browse_thread/thread/9f102ad2346f73e7/?hl=en#

Constant[c,d th,ph] ;

(*  th, ph are spherical cords of tip of tube  *)  ;

cp = Cos[ph] ; sp = Sin[ph] ; cth = Cos[th] ; sth = Sin[th] ;

d1 = Sqrt[(x + d cp cth + c )^2 + ( y + d cp sth )^2 + (d sth)^2 ]

d2 =Sqrt[(x - d cp cth - c )^2 + ( y - d cp sth )^2 + (d sth)^2 ]

FullSimplify[ d1 + d2 + 2 d - 2 a == 0] ;

When d =0, algebraic/trig simplification to ellipse is common.

Request help for bringing to standard form.

Regards,
Narasimham