Re: Ellipse equation simplification on Mathematica:

*To*: mathgroup at smc.vnet.net*Subject*: [mg77125] Re: Ellipse equation simplification on Mathematica:*From*: Narasimham <mathma18 at hotmail.com>*Date*: Mon, 4 Jun 2007 03:52:48 -0400 (EDT)*References*: <f2emof$35h$1@smc.vnet.net><200706010641.CAA25336@smc.vnet.net>

On Jun 2, 1:37 pm, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote: > This can't be true without some additional assumptions, since, as I > showed in my reply: > > Expand[(-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 == 0 /. > {a -> 181, c -> -(39/10), d -> 100, cp -> 1}] > > (267421*x^2)/100 - 6561*y^2 - 1754549181/100 == 0 > > which is a hyperbola. However, in this case the original equations > have no solutions. a > c > 0, 2c is the inter focal distance same as for the standard ellipse. Narasimham > Andrzej Kozlowski > > On 1 Jun 2007, at 15:41, Narasimham wrote: > > > 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

**References**:**Re: Ellipse equation simplification on Mathematica:***From:*Narasimham <mathma18@hotmail.com>