# How do you classify the conic -6x^2+4y^2+2x+9=0?

May 20, 2017

Here is a helpful reference Conic Section

#### Explanation:

Using the General Cartesian Form in the reference,

$A {x}^{2} + B x y + C {y}^{2} + D x + E y + F = 0$

, to compare to the given equation,

$- 6 {x}^{2} + 4 {y}^{2} + 2 x + 9 = 0$

, we observe that $A = - 6 , B = 0 , C = 4 , D = 2 , E = 0 \mathmr{and} F = 9$

We can you the discriminant, ${B}^{2} - 4 A C$, to classify the conic section:

${B}^{2} - 4 A C = {0}^{2} - 4 \left(- 6\right) \left(4\right) = 96$

According to the reference this represents a hyperbola.