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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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 + ____ + _____
2(x^2 - (9/2)x + _____) + 4(y^2 + 2x + _____) = 16 + 2(____) + 4(_____)
Fill in the blanks.
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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.