$\text{ If distance between two parallel tangents having slope }m\text{ drawn to the hyperbola }\frac{x^2}{9}-\frac{y^2}{49}=1\text{ is }2\text{ then the value of }\left|m\right|\text{ is }$

Tangents to hyperbola having slope m are

$\begin{array}{l}y=mx\pm \sqrt{9m^2-49}\\ \text{ Distance between tangents is }2\text{ . }\\ \Rightarrow \frac{2\sqrt{9m^2-49}}{\sqrt{1+m^2}}=2\\ \Rightarrow 9m^2-49=1+m^2\\ \Rightarrow 8m^2=50\\ \Rightarrow m=\pm \frac{5}{2}\end{array}$