Quadratic Equation:
ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0

Properties of Quadratic Equation:

if a = b = 0 -> Straight Line
if a = b != 0 -> Circle
if D = 0 -> Pair of Lines
Now for D != 0 & for Z :
= 0 -> Parabola
< 0 -> Ellipse
> 0 -> Hyperbola

D = abc + 2gh - af^2 - bg^2 - ch^2
Z = h^2 - ab