Re: Graphing Rotation of ellipse

To: CALC-TI@LISTS.PPP.TI.COM
Subject: Re: Graphing Rotation of ellipse
From: erikanielsen@HOTMAIL.COM
Date: Wed, 15 Apr 1998 09:46:57 -0600
Organization: Deja News - The Leader in Internet Discussion
References: <6h16uo$462s$1@newssvr04-int.news.prodigy.com>
Reply-To: erikanielsen@HOTMAIL.COM
Xref: paladin.american.edu bit.listserv.calc-ti:22429

Dear William,

Try this.

In POLAR mode, enter the equation (write theta instead of t, square root
instead of sqrt)

r1(t)=4/sqrt(7+2(sin t)^2-3 sqrt(3) sin (2t) )

Set the window: Xmin=-3, Xmax=3, Ymin=-2, Ymax=3, tMin=0, tMax=2pi

Let me know how it works.

Curves defined by equations of (x,y), not of the form y=f(x), are very hard to
draw. TI calculators cannot do it directly. Maple has a command for implcit
curve plotting, but if you try it, you will be rather disapionted with the
results.

If you want to draw a curve like this on a TI, you have to use some "tricks"
and recast the equation as a polar equation, or as a pair of parametric
equations. Of course, for ellipses you have also the Analytical Geometry
approach, which uses matrices, eigenvalues and eigenvectors. In this
particular case though, I think the above approach is simpler.

Greetings,

Erika

In article <6h16uo$462s$1@newssvr04-int.news.prodigy.com>,
  TMZJ41A@prodigy.com (William Walters) wrote:
>
> Can anyone tell me how to graph the following ellipse:
>
>    7X^2 - 6sqrt(3)XY + 9Y^2 - 16 = 0
>
> I have a TI-82 and a TI-83 for classroom demos and a personal TI-85, but
> would prefer not to use it.  If there is no way on the TI's, is there a
> graphical program for the computer?
>
> Bill Walters
> Poca High School
> Poca, WV
>
>

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References:

Graphing Rotation of ellipse

From: William Walters <TMZJ41A@PRODIGY.COM>