# (3x^2)-(2y^2)-9x+4y-8=0 Graph and find all applicable points (center, vertex, focus, asymptote)?

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I got the equation to be #(x-3/2)^2/(12/67)-(y+1)^2/(8/67)# =1

I got crazy fractions for vertex and a focus that isn't even inside the curves, so I'm pretty sure my answer is incorrect.

I got the equation to be

I got crazy fractions for vertex and a focus that isn't even inside the curves, so I'm pretty sure my answer is incorrect.

##### 1 Answer

Nothing crazy about fractions you got. But see the difference with what I got.

#### Explanation:

graph{(3x^2)-(2y^2)-9x+4y-8=0 [-10, 10, -4, 6]}

Paring

Rearranging

Making terms in the bracket perfect squares

Taking the constant terms out of bracket

Dividing both sides with

Comparing with general expression of hyperbola

We get

from values of

asymptotic lines as:

And remaining items: foci and vertices

Cheers.