Hyperbola

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