Convergence radius for the Taylor series of a function of two variables.

For a single variable function expanded about the point $x_0$, the radius of convergence is the radius of the largest disk around $x_0$ in which $f(z)$ is analytic. For example, the radius of convergence of $frac{1}{(1+x^2)}$, when expanded about $x_0=1,$ is equal to $sqrt{2}$, because the poles of $frac{1}{(1+z^2)}$ are at $pm j$, and $sqrt{2}$ is the distance of $x_0=1$ from $pm j$.

How do we calculate the radius of convergence for a function of two variables, for example
$f(x,y)=frac{1}{[(1+x^2)*(1+y^2)]}$ expanded about ($x_0$,$y_0$)?!