Which conic section is represented by the equation shown below? 2x^2-9x+4y^2+8x=16 A.) hyperbola B.) Parabola C.) Circle D.) Ellipse

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Which conic section is represented by the equation shown below? 2x^2-9x+4y^2+8x=16 A.) hyperbola B.) Parabola C.) Circle D.) Ellipse

Mathematics
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There is a formula for that, or you can resort to Completing the Square (in both x and y). You choose. (2x^2 - 9x + _____) + (4y^2 + 8x + _____) = 16 + ____ + _____ Or 2(x^2 - (9/2)x + _____) + 4(y^2 + 2x + _____) = 16 + 2(____) + 4(_____) Fill in the blanks.
Making this a elipse correct ?
You tell me.

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I don't know for sure that's why I was asking you...
Well, you need to know for sure. I won't be there on your exam. What are the characteristics? Is there a "-" between the x-stuff and the y-stuff? If "no", then it's not an hyperbola. Is the coefficient on x^2 the same as the coefficient on y^2? If "no", then it's not a circle. Where does that leave us?
This leaves us with an elipse
Done! Now, where is your lack of confidence? P.S. There are some really weird degenerate conic sections where you get parallel lines or just a point.

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