User:Rlendog/Sandbox7

$$   {1-\rho^2 }  $$

$$ 2 ( \frac {x_1^2}{\sigma_1^2} - \frac{2 \rho x_1 x_2}{\sigma_1 \sigma_2} +  \frac {x_2^2}{\sigma_2^2} )  $$

$$  \frac { 2 ( \frac {x_1^2}{\sigma_1^2} - \frac{2 \rho x_1 x_2}{\sigma_1 \sigma_2}  +  \frac {x_2^2}{\sigma_2^2} )} { {1-\rho^2 } }  $$

$$ \sqrt { \frac { 2 ( \frac {x_1^2}{\sigma_1^2} - \frac{2 \rho x_1 x_2}{\sigma_1 \sigma_2}  +  \frac {x_2^2}{\sigma_2^2} )} { {1-\rho^2 } } }$$