Solution
= Solution
By the implicit <derivative> formula,
$$
h'(0)=-\frac{f_x(0,0)}{f_y(0,0)}=-1.
$$
All sufficiently near points of the curve have $y=h(x)$, and the only such point with $x=0$ is the origin itself. Therefore for the punctured approach along the curve,
$$
\boxed{\lim_{\substack{(x,y)\to(0,0)\\(x,y)\in C,\ (x,y)\neq(0,0)}}\frac yx
=\lim_{x\to0}\frac{h(x)-h(0)}x=h'(0)=-1.}
$$