A common tangent T to the curves C_1: x^2/4+y^2/9=1 and C_2: x^2/42-y^2/143=1 does not pass through the fourth quadrant. If T touches C_1 at (x_1,…

A common tangent T to the curves $\displaystyle \mathrm{C}_1: \frac{x^2}{4}+\frac{y^2}{9}=1$ and $\displaystyle \mathrm{C}_2: \frac{x^2}{42}-\frac{y^2}{143}=1$ does not pass through the fourth quadrant. If T touches $\displaystyle \mathrm{C}_1$ at $\displaystyle \left(x_1, y_1\right)$ and $\displaystyle \mathrm{C}_2$ at $\displaystyle \left(x_2, y_2\right)$, then $\displaystyle \left|2 x_1+x_2\right|$ is equal to \_\_\_\_.