The Chain Rule & Implicit Differentiation · Superchallenge problem

A smooth function $f(x,y)$ on $x > 0$ is homogeneous of degree $2$: $f(\lambda x, \lambda y) = \lambda^2 f(x,y)$ for all $\lambda > 0$. You know only $f(1,2) = 5$ and $f_x(1,2) = 4$. Find $f_y(3,6)$.