Expert: Richard J. Raridon - 4/18/2005

Question
3x^2 + 5x + 3y^2 + 4y + 7 = 0

How do I find out whether the equation is a parabola, circle, ellipse, or hyperbola?

Answer
A parabola would have only one variable squared.
A circle would be symmetric.
A hyperbola would have either -3x^2 or -3y^2.  
If that were a -7, you'd have an ellipse but the way it is, it's an imaginary function.
You can determine that by re-writing it
3x^2 +5x +7 = -3y^2 -4y
If you set y=0, with an ellipse you'd get two points on the x-axis.  If you try that here you get imaginary values.  The same thing happens with x=0