# 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?

Jan 30, 2018

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 ${x}^{2} , x y , \mathmr{and} {y}^{2}$.
Let $\Delta = {B}^{2} - 4 A C$ be the discriminant.
Then $\Delta = 36 - 4 \left(9\right) \left(1\right) = 0$.

Since the discriminant is zero, this is a parabola.