JEE Main 2022 · 27 Jul · Shift 2, Mathematics question 29

A common tangent T to the curves $C_1:\dfrac{x^2}4+\dfrac{y^2}9=1$ and $C_2:\dfrac{x^2}{42}-\dfrac{y^2}{143}=1$ does not pass through the fourth quadrant. If T touches $C_1$ at $(x_1,y_1)$ and $C_2$ at $(x_2,y_2)$, then $|2x_1+x_2|$ is equal to ______.