Consider a hyperbola H having centre at the origin and foci on the x-axis. Let \({C}_{1}\) be the circle touching the hy…

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 the origin. Let \({C}_{2}\) 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 isEndFragment

[JEE Main 2024, 04 Apr (Shift 2)]