Answer
Discontinuous for the unit circle $x^{2}+y^{2}=1$
Work Step by Step
Use the maple command to plot the graph of the function as depicted below:
From the above graph we observe a circular break in the graph, which corresponds to a unit circle for which the function is discontinuous.
As the function $f(x,y)=\frac{1}{1-x^{2}-y^{2}}$ is a rational function, it is continuous except where $1-x^{2}-y^{2}=0$ or $x^{2}+y^{2}=1$
Therefore, the function $f(x,y)=\frac{1}{1-x^{2}-y^{2}}$ is discontinuous for the unit circle $x^{2}+y^{2}=1$
