Question

How do use the discriminant test to determine whether the graph `x^2+2xy-3y^2+5x+6y-100=0` whether the graph is parabola, ellipse, or hyperbola?

Answer 1

Given: `Ax^2+Bxy+Cy^2+Dx+Ey+F=0`
The discriminant is, `del=B^2-4AC`
If `del<0`, then, if `B=0 and A=D`, a circle. Otherwise, an ellipse.
If `del=0`, then a parabola
If `del>0`, then a hyperbola.

Explanation:

Given: `x^2+2xy-3y^2+5x+6y-100=0`

`A = 1`, `B=2`, and `C= -3`

`del = 2^2-4(1)(-3)`

`del = 16`, then it is a hyperbola.