# What is the general equation for a conic section?

$A {x}^{2} + B x + C {y}^{2} + D y + E = 0$
When $A$ or $C$ is 0, the equation is that of a parabola.
When $A$ and $C$ have the same value (including signs), the equation is that of a circle.
When $A$ and $C$ have the same sign, the equation is that of an ellipse
When $A$ and $C$ have different signs, the equation is that on a hyperbola