Question

How do use the discriminant test to determine whether the graph `9x^2+6xy+y^2+6x-22=0` whether the graph is parabola, ellipse, or hyperbola?

Answer 1

Let's set it up...

Explanation:

In the form that your section is in,
A = 9, B = 6, and C = 1.
These are the lead coefficients of `x^2, xy, and y^2`.
Let `Delta = B^2 - 4AC` be the discriminant.
Then `Delta = 36 - 4(9)(1) = 0`.

Since the discriminant is zero, this is a parabola.