Standardform: ax² + bx + cy² + dy + e= 0
If you have an equation like 4x² + 4y²=36 The equation is a circle, because a=c
Example of a circle
If a or c equals 0 the equation is a parabola (for example: 2x² + 4y= 3)
Example of a parabola:
If a or c have different signs the equation is a hperbola ( for example: 4x² - 4y²= 12)
Example of a hyperbola
If you have an equation like 4x² + 3y²= 25 the equations is an ellipse, because a is not equal to c and the signs are the same
Example of an ellipse
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