Circle Discriminant
In Homogeneous coordinates (x_1,x_2,x_3), the equation of a circle C is
| a(x_1^2+x_2^2)+2fx_2x_3+2gx_1x_3+cx_3^2=0. |
The discriminant of this circle is defined as
and the quadratic form q(C)=ac-f^2-g^2 is the basic invariant.
See also
Conic Section DiscriminantExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Barth, W. and Bauer, T. "Poncelet Theorems." Expos. Math. 14, 125-144, 1996.Referenced on Wolfram|Alpha
Circle DiscriminantCite this as:
Weisstein, Eric W. "Circle Discriminant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CircleDiscriminant.html