Bound on probability of bi-variate chi-square distribtuion

Question

If I have two random variables $u_1 = x_1^2$ and $u_2 = x_2^2$ where $x_1,x_2 \sim \mathcal{N}(0,1)$ and $E(x_1x_2) = \rho$. The what is the pdf or bound on the pdf of $P(u_1<c,u_2>c)$? Edit: The covariance matrix is $\sum$ where $\sum (1,1) =\sum (2,2) =1$ and $\sum (1,2) =\sum (2,1) = \rho$.