       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

```

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