# 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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**Conic Sections and Quadric Surfaces**

**RE: Conic Sections and Quadric Surfaces**