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

Question

tkhunny · Answer

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.

lilmike234 · Answer

Making this a elipse correct ?

tkhunny · Answer

You tell me.

lilmike234 · Answer

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

tkhunny · Answer

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?

lilmike234 · Answer

This leaves us with an elipse

tkhunny · Answer

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.