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Re: Ellipse equation simplification on Mathematica:

• To: mathgroup at smc.vnet.net
• Subject: [mg76222] Re: Ellipse equation simplification on Mathematica:
• From: Narasimham <mathma18 at hotmail.com>
• Date: Fri, 18 May 2007 06:06:09 -0400 (EDT)
• References: <f2emof$35h$1@smc.vnet.net>

 Reference is made to:

http://groups.google.co.in/group/geometry.puzzles/browse_thread/threa...

 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] ;

(*  earlier typo corrected *)

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

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

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

 When d = 0, algebraic/trigonometric simplification brings about
common ellipse form:

(x/a)^2 + y^2/(a^2-c^2) = 1

 Request help for bringing to standard form involving constants a,c
and the new tube length constant d.

 Regards,
 Narasimham

• Follow-Ups:
  • Re: Ellipse equation simplification on Mathematica:
    • From: Narasimham <mathma18@hotmail.com>
  • Re: Re: Ellipse equation simplification on Mathematica:
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>