Re: Ellipse equation simplification on Mathematica:

*To*: mathgroup at smc.vnet.net*Subject*: [mg77032] Re: Ellipse equation simplification on Mathematica:*From*: Narasimham <mathma18 at hotmail.com>*Date*: Fri, 1 Jun 2007 02:41:13 -0400 (EDT)*References*: <f2emof$35h$1@smc.vnet.net><200705300929.FAA13381@smc.vnet.net>

On May 31, 12:19 pm, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote: > On 30 May 2007, at 18:29, 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 The above can be simplified, and they are shown capable of being cast into canonical form of ellipses : (x/aEff)^2 + y^2/(aEff^2 - cEff^2) = 1 For case x-axis parallel tube cp = 1, forming trapeziums at each stage: aEff = (a - d), cEff = (c + d). For case x-axis perpendicular to tube cp = 0: aEff = (a - d) V, cEff = c V where V = Sqrt((a^2 -2 a d -c^2)/(a^2 -2 a d -c^2 + d^2) ) 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>