wlw2286@isc.rit.edu (W.L. Ware ) (11/02/90)
I would like a program that when given the formula for a conic section, would identify it (i.e. parabola, ellipse, hyperbola) and then find its center, directrix, axis, major axis, minor axis, etc ... And then, although not to big a deal auto-scale and graph it. Does anyone know if a program like this exists? Or if not could it be written easily Lance -- ************************************************************************ *W.L.Ware LanceWare SYSTEMS* *WLW2286%ritvax.cunyvm.cuny.edu Value Added reseller* *WLW2286%ultb.isc.rit.edu Mac and IBM Access. *
jmorriso@ee.ubc.ca (John Paul Morrison) (11/03/90)
Identifying a general conic section from an equation like a*x^2 + b*y^2 + c*x*y + d*x + e*y + f = 0 isn`t that complicated, it just takes a bit of nummber crunching. You should look at a few linear algebra books. You have to set up the above equation in matrix form, and squish out some eigenvalues of a 2*2 matrix, which isn't tough. If anyone is desperate enough I can dig up the book and recant the exact procedure.
akcs.kolstad@hpcvbbs.UUCP (Joel Kolstad) (11/06/90)
Actually, identifying a conic in the form of ax^2+bxy+cy^2+dx+ey+f=0
involvves very little algebra. You just take a look at the
discriminant. (Which is b^2-4ac).
If the discriminent is <0, the graph is an ellipse.
If the discriminant is =0, the graph is a parabola.
If the discriminant is >0, the graph is a hyperbola.
Note that this doesn't take into account degenerative cases --
ellipses can turn into circles, points, etc. -- and the other graphs
can degenerate too.
There's a so called "extended discriminent" that allows you to predict
when things degenerate, but as I recall, it's rather messy and you're
just about better to graph the equation if you're unsure.
For more info on this (aren't conic sections fun?), see a Calculus text
that includes analytic geometry (many do), or simply a plain analytical
geometry book.
Have fun!
Note to HP: (Are you listening, Bill Wickes?) the next machine you make,
let the plotter's function menu have things operate on more that
"FUNCTION" type functions! (For example, it isn't that hard to plot the
derivitive of a polar equation! Or a parametric equation, like these
conic sections can be written as!) :-)
---Joel Kolstad