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Conic Section Discriminant

The discriminant of the general conic section

ax_1^2+bx_2^2+cx_3^2+2fx_2x_3+2gx_1x_3+2hx_1x_2=0

is defined as

Delta=|a h g; h b f; g f c|=abc+2fgh-af^2-bg^2-ch^2.

If b=a and g=h=0, then simplifies to the circle discriminant.

See also

Circle Discriminant

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References

Salmon, G. Conic Sections, 6th ed. New York: Chelsea, p. 266, 1960.

Referenced on Wolfram|Alpha

Conic Section Discriminant

Cite this as:

Weisstein, Eric W. "Conic Section Discriminant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConicSectionDiscriminant.html

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