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RE: Conic Sections and Quadric Surfaces

you only have 5 points. you have a familly of conic sections that can go
through those points:

data = {{-1,0},{0,1},{2,2},{1,-1}, {0,-3}};

Show[Graphics[Point /@ data],AspectRatio->1,Axes->True]

define the function, but assume a = 1 f[{x_,y_}]:= x^2 + b x y + c y^2 +
d x + e y + f;

sol = Solve[ f[#]==0& /@ data,{b,c,d,e,f}][[1]];

and you can plot it:

<< Graphics`ImplicitPlot`

ImplicitPlot[f[{x,y}]==0 /. sol , {x,-2,3}]

good luck!


>-----Original Message-----
>From: []
>Sent:	Wednesday, February 18, 1998 5:33 PM
>Subject:	[mg11082] Conic Sections and Quadric Surfaces
>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

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