Identiying Quadratic Equations

If a=c then the equation is a circle: 2x² + 2y²= 36

If  a or c equals 0 then the equation is a parabola: x² + 2y= 6

If a and c have different signs then the equation is a hyberbola: 3x² - 3y²= 12

If  a is not equal to c but the signs are the same then the equation is an ellipse: 3x² + 2y²= 36