## Curvature at a point

Given an equation Z = aX^2 + 2bXY + cY^2 + dX + eY + f. (a-f are coefficients)
I am trying to find the curvature at a given point.
I have the gradient as [2ax + 2by +d , 2bx + 2cy + e]
The normal unit vector as
[2ax + 2by +d , 2bx + 2cy + e] / sqrt((2ax + 2by +d)^2 + (2bx + 2cy + e)^2)
and the hessian matrix as
Code:
[2a  2b]
[2b  2c]
Can anyone confirm if I am correct thusfar, and how to get the gaussian curvature k1*k2 from here?