What is the general equation for a conic section?

The general equation of a conic section is in the form

#Ax^2 + Bx + Cy^2 + Dy + 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