Path: utzoo!attcan!uunet!zaphod.mps.ohio-state.edu!sdd.hp.com!hp-pcd!hpcvra!rnews!hpcvbbs!akcs.kolstad
From: akcs.kolstad@hpcvbbs.UUCP (Joel Kolstad)
Newsgroups: comp.sys.handhelds
Subject: Re: Program wanted for conic sections.
Message-ID: <273646df:1039.2comp.sys.handhelds;1@hpcvbbs.UUCP>
Date: 6 Nov 90 05:40:12 GMT
References: <1990Nov1.180343.7086@isc.rit.edu> <1990Nov2.131309@ee.ubc.ca>
Lines: 30


 
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