Consider a hyperbola H having centre at the origin and foci on the x-axis. Let $\mathrm { C } _ { 1 }$ be the circle touching the hyperbola H and having the centre at the origin. Let $\mathrm { C } _ { 2 }$ 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 $C _ { 1 }$ and $C _ { 2 }$ are $36 \pi$ and $4 \pi$, respectively, then the length (in units) of latus rectum of H is (1) $\frac { 14 } { 3 }$ (2) $\frac { 28 } { 3 }$ (3) $\frac { 11 } { 3 }$ (4) $\frac { 10 } { 3 }$
Consider a hyperbola H having centre at the origin and foci on the x-axis. Let $\mathrm { C } _ { 1 }$ be the circle touching the hyperbola H and having the centre at the origin. Let $\mathrm { C } _ { 2 }$ 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 $C _ { 1 }$ and $C _ { 2 }$ are $36 \pi$ and $4 \pi$, respectively, then the length (in units) of latus rectum of H is\\
(1) $\frac { 14 } { 3 }$\\
(2) $\frac { 28 } { 3 }$\\
(3) $\frac { 11 } { 3 }$\\
(4) $\frac { 10 } { 3 }$