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 asCan anyone confirm if I am correct thusfar, and how to get the gaussian curvature k1*k2 from here?Code:[2a 2b] [2b 2c]