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.