Let L_1 be a line in the y z - plane with y and z intercepts 1/4 and 1/C(C>0) respectively. Let L_2 be the line in the x z - plane with x and z…

Let $\displaystyle L_1$ be a line in the $\displaystyle y z$ - plane with $\displaystyle y$ and $\displaystyle z$ intercepts $\displaystyle \frac{1}{4}$ and $\displaystyle \frac{1}{C}(C>0)$ respectively. Let $\displaystyle L_2$ be the line in the $\displaystyle x z$ - plane with $\displaystyle x$ and $\displaystyle z$ intercepts $\displaystyle \frac{1}{3}$ and $\displaystyle -\frac{1}{C}$ respectively. If the shortest distance between $\displaystyle L_1$ and $\displaystyle L_2$ is $\displaystyle \frac{1}{5}$, then $\displaystyle C^2$ is equal to \_\_\_\_.