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

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Answer 1 · 2017-05-20T20:00:16

Here is a helpful reference Conic Section

Using the General Cartesian Form in the reference,

$Ax^2+Bxy+Cy^2+Dx+Ey + F = 0$

, to compare to the given equation,

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

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

We can you the discriminant, $B^2-4AC$ , to classify the conic section:

$B^2-4AC = 0^2-4(-6)(4) = 96$

According to the reference this represents a hyperbola.

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