2010 AMC 12A Problem 13

For how many integer values of k do the graphs of x^2+y^2=k^2 and xy = k not intersect?

\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 8

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.