Both x and y are squared, and they have the same number in front of them…and they are added. This is a Circle.

x^2 + 4y^2 =9

The equation above doesn’t have the same number in front of the variables, so it can’t be a circle. But they are still squared and added, so it’s an ellipse.

29x^2 – 29y^2 =700

Even though these are both squared, and have the same number in front, it’s not a circle, because the terms are subtracted. That means it’s a hyperbola.

One more,… if only x is squared, but not y, then it’s a parabola.