Circle Discriminant

In Homogeneous coordinates (x_1,x_2,x_3), the equation of a circle C is


The discriminant of this circle is defined as

 Delta=|a 0 g; 0 a f; g f c|=a(ac-f^2-g^2),

and the quadratic form q(C)=ac-f^2-g^2 is the basic invariant.

See also

Conic Section Discriminant

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Barth, W. and Bauer, T. "Poncelet Theorems." Expos. Math. 14, 125-144, 1996.

Referenced on Wolfram|Alpha

Circle Discriminant

Cite this as:

Weisstein, Eric W. "Circle Discriminant." From MathWorld--A Wolfram Web Resource.

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