JEE Main 2024 — Hyperbola Question with Solution

Consider a hyperbola $$\mathrm{H}$$ having centre at the origin and foci on the $$\mathrm{x}$$-axis. Let $${\mathrm{C}}_1$$ be the circle touching the hyperbola $$\mathrm{H}$$ and having the centre at the origin. Let $${\mathrm{C}}_2$$ be the circle touching the hyperbola $$\mathrm{H}$$ 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 $$\mathrm{H}$$ is