The general form of a second-degree quadratic in 2 variables is
We have to check the expression to determine the type of conic.
If , then we have a hyperbola.
If , then we have a parabola.
If , then we have either a circle or an ellipse. If B = 0 and A = C, then we have a circle. Otherwise, it's an ellipse.
Now try your problem. B = 0 and A = 2...