Let one focus of the hyperbola \(\mathrm{H}:\frac{{\mathrm{x}}^{2}}{{\mathrm{a}}^{2}}-\frac{{\mathrm{y}}^{2}}{{\mathrm{b…

Let one focus of the hyperbola \(\mathrm{H}:\frac{{\mathrm{x}}^{2}}{{\mathrm{a}}^{2}}-\frac{{\mathrm{y}}^{2}}{{\mathrm{b}}^{2}}=1\) be at \((\sqrt{10},0)\) and the corresponding directrix be \(\mathrm{x}=\frac{9}{\sqrt{10}}\). If \(e\) and \(l\) respectively are the eccentricity and the length of the latus rectum of \(H\) , then \(9\left({\mathrm{e}}^{2}+l\right)\) is equal to:

[JEE Main 2025, 2 Apr (Shift 1)]