Re: Graphing Rotation of ellipse

To: CALC-TI@LISTS.PPP.TI.COM
Subject: Re: Graphing Rotation of ellipse
From: RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU>
Date: Wed, 15 Apr 1998 10:34:16 -0500
Reply-To: RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU>

>  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

There's been a fair bit of discussion on this list over the years of strategies
for plotting general relations in x and y on the TI.  The usual approach taken
is to sweep over the entire visible screen, testing the relation pixel-by-pixel
and turning on the pixels for which the result is TRUE.

But you've got a special case here.  For each X-value between Xmin and Xmax,
substituting the present value of X gives you a quadratic expression in Y,
which can be immediately solved to tell you the relevant 2, 1 or 0 pixels to be
turned on for that column, so that you could get by with a single loop -- much
faster.  You could "beef up" the display by making a second pass in the
Y-direction, if you wanted.

This means writing a program, of course.  All the info you need to do this is
in the manual.  I don't know if it would be worth your time to check the
archives to see if there is such a program (or one that is close enough to
adapt) already there.  Perhaps you have done this already.

RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623

>>>> The plural of mongoose begins with p. <<<<

P.S. Again looking at your particular case, if your equation is viewed as a
quadratic in y, the discriminant works out to be 144(4-xx), so that all the
"action" happens between -2 and 2.  There's always some value to "off-line"
analysis to reduce the amount of work associated with a particular calculation
task -- you almost never want to just hand a problem "blind" to the calculator.
Is your goal here just to plot this one particular curve, or to develop the
capability to plot such curves in general?  If the latter, you might be able to
get your calculator to cooperate in such pre-analysis.