Discriminant of a quadratic equation in 2 variables

[Ashu2912]

Main Question or Discussion Point

Can anyone tell me how to calculate the discriminant of a general equation of 2 degree in 2 variables, ax$^{2}$+by$^{2}$+2gx+2fy+2hxy+c=0? Thanks!!!

 

[Stephen Tashi]

I've never seen a textbook that defined the descriminant for a polynomial of two variables. How do your materials define it?

 

[Ashu2912]

In my text it is defined as abc+2gfh-a(f sq.)-b(g sq.)-c(h sq.). I just want to know how is it derived and what is it's significance and implication....

 

[Stephen Tashi]

What is the title of your text?

Wolfram has a page on the discriminant of a quadratic curve and it gives a different formula:
http://mathworld.wolfram.com/QuadraticCurveDiscriminant.html