SOLUTION: determine whether the following equations are parabolas, circles, ellipses or hyperboles 2x^2+6y^2=18 4x^2=36y^2=144 y^2-x^2+6x-4y-6=0 Please I really need this!!

Question 875379: determine whether the following equations are parabolas, circles, ellipses or hyperboles
2x^2+6y^2=18

4x^2=36y^2=144

y^2-x^2+6x-4y-6=0

Please I really need this!! Thank you 1
Answer by josgarithmetic(39621) (Show Source): You can put this solution on YOUR website!
Your second equation is not written correctly; but you should be able to project forward by one or two steps for the first equation and the third equation and know which conic each is. You need to know how to recognize the standard forms of the the conic section equations.

2x^2+6y^2=18;
Divide both sides by 18, and you know this is an ellipse.

y^2-x^2+6x-4y-6=0;
You have some y^2-x^2, so you know this will be a hyperbola.
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