fitting an ellipse

[Streph Treadway]

Hi, all,

I am currently teaching a unit on conic section in my high school
mathematics class.  I plan to use octave, gnuplot and epstk so that my
students can generate ellipses by choosing various values for center
coordinates, semi-major axis and eccentricity.

To plot ellipses, I have been using commands like:

t=[0:.01:2*pi];
x=a*sin(t);
y=b*cos(t);
plot(x, y);

where a and b are the semi-major and simi-minor axes of the ellipse.

I'd like to also have my students try an experiment duplicating, in 2
dimensions rather than 3, Gauss' determination of the orbit of Ceres.  I
have been experimenting with leasqr recently and quite enjoy it, but am
stumped when it comes to fitting two functions simultaneously to the
same set of data.  I suppose I could fit each trig function separately,
but I would love to have the very instructively graphic output of leasqr
produce an ellipse.

Any suggestions?

Yours,

Streph



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