The figure shows level sets $f(x,y) = 1$ and $g(x,y) = 0$ for two different functions $f(x,y)$ and $g(x,y)$. Assuming that the graphs of $f$ and $g$ are both elliptic paraboloids with $x=0$ and $y=0$ as planes of reflection symmetry and that $f(0,0) = 0$ and $g(0,0) = 1$, find formulas for these functions.

$f(x,y) =$

$g(x,y) =$