Quadratic Functions

This is how to identify Quadratic Functions:
The standard Form is: ax² + bx + cy² + dy + e= 0
Circle Equation- A=C
So for example X²+Y²=9. So the center is at the origin. And the radius is 3.

Parabola- A or C = 0
For example: X²+4X+4. So the intercepts are at 2 on the x axis and 4 on the y.

Hyperbola- A or C has different signs from each other
For example: (X²/A²) - (Y²/B²) = 1
The two red lines are asymptotes. Or lines the hyperbola will continue to try to reach but will never reach.
Ellipse- A is not equal to C. However the signs are still the same.
For example: x²/16 + y²/4 = 1