The Chain Rule & Implicit Differentiation · Superchallenge problem

A smooth function $f(x,y)$ has, at a point $P$: $f_x = 3$, $f_y = 4$, $f_{xx} = 1$, $f_{xy} = 2$, $f_{yy} = -1$. Using implicit differentiation, find the curvature at $P$ of the level curve of $f$ that passes through $P$.