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Question Id : 14339 | Context : JEE Main 2024 (4 April Evening Shift)
Consider a hyperbola $\text{H}$ having centre at the origin and foci on the x-axis. Let $C_1$ be the circle touching the hyperbola $\text{H}$ and having the centre at the origin. Let $C_2$ be the circle touching the hyperbola $\text{H}$ 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 $\text{H}$ is:


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