Find the osculating circle $C$ of the parabola $x^2+y=0$ at the origin $(0,0)$. Find a function $f(x,y)$ such that $C$ is a level curve of $f$.
What I have done so far was to find the quadratic equation for osculating circle. However, I did not understand how that equation correlates with level curve. If remember correctly, level curve meant to be $f(x,y)$ being a constant number.