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MathGroup Archive 1998

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Re: Conic Sections and Quadric Surfaces


  • To: mathgroup@smc.vnet.net
  • Subject: [mg11088] Re: Conic Sections and Quadric Surfaces
  • From: weber@math.uni-bonn.de (Matthias Weber)
  • Date: Sun, 22 Feb 1998 14:55:13 -0500
  • Organization: RHRZ - University of Bonn (Germany)
  • References: <6cghv9$skg@smc.vnet.net>

In article <6cghv9$skg@smc.vnet.net>, mavalosjr@aol.com (MAvalosJr)
wrote:

> Dear Sir:
> Ref: Introduction to Linear Algebra- 4th ed. Johnson,Riess and Arnold
> (page 35)
> 
> Find the equation of the conic section passing through the five points
> (-1,0),(0,1),(2,2),(1,-1), (0,-3). Display the graph of the conic.
> 
> When I try to set up the augmented matrix I get two (2) indeterminate
> rows which
> prevents my proceeding with the method outlined in the textbook Linear
> Algebra with Mathematica by E. Johnson page 58 to 59. How can  I get
> around this?The equation to satisfy (an ellipse) is ax^2 + bxy + cy^2 +
> dx + ey + f =0.  Is there some other technique I can use to find the
> equation given sevral points?
> I am presently playing around with Fit[ data,{etc}] but I only know how
> to fit quadratics. Thank you in advance.
> Manuel Avalos
> MAvalosjr@aol.com

conic[{x_, y_}]:=a x^2 + b x y + c y^2 + d x + e y + f ==0

Map[conic,{{-1,0},{0,1},{2,2},{1,-1}, {0,-3}}]

Solve[%,{a,b,c,d,e,f}]

This shows how live is changing: One hasn't to teach anymore to solve
linear equations, but to teach how to use Mathematica for this. Sigh.
Even if it is vain: My general recipe is: If you don't know how to
solve a problem by hand, it is unlikely that you can do it with
Mathematica. And if you know, there is a slight chance that you can do
the next slightly more complicated  problem with Mathematica, provided
there are only technical obstacles to overcome. So better do it first
by hand...


Matthias



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