Question

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

Answer 1

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.

Answer 2

Making this a elipse correct ?

Answer 3

You tell me.

Answer 4

I don't know for sure that's why I was asking you...

Answer 5

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?

Answer 6

This leaves us with an elipse

Answer 7

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.