Consider a hyperbola H having centre at the origin and foci on the x -axis. Let C_1 be the circle touching the hyperbola H and having the centre at…

Consider a hyperbola H having centre at the origin and foci on the x -axis. Let $\displaystyle \mathrm{C}_1$ be the circle touching the hyperbola H and having the centre at the origin. Let $\displaystyle \mathrm{C}_2$ be the circle touching the hyperbola H at its vertex and having the centre at one of its foci. If areas (in sq units) of $\displaystyle \mathrm{C}_1$ and $\displaystyle \mathrm{C}_2$ are $\displaystyle 36 \pi$ and $\displaystyle 4 \pi$, respectively, then the length (in units) of latus rectum of H is