Identifying Quadratic Functions

The standard form of a quadratic function is ax² + bx + cy² + dy + e= 0
A quadratic function is a circle when a=c.
A quadratic function is a parabola when either a or c equals 0.
A quadratic function is a hyperbola when a and c have different signs.
A quadratic function is an ellipse when a and c have the same sign, but a is not equal to c.

Example of a circle:

Example of a parabola:

Example of a hyperbola:

Example of an ellipse: