If (5,12), (24,7) are the foci of the hyperbola passing through origin, then its eccentricity is

$$\begin{gathered} \mathrm{Given} \mathrm{foci} \mathrm{S}=(5, 12), {\mathrm{S}}^1=(24, 7) \\ \mathrm{let} \mathrm{P}=(0, 0) \mathrm{be} \mathrm{point} \mathrm{on} \mathrm{hyperbola} \\ \mathrm{In} \mathrm{hyperbola} \left|\mathrm{SP}-{\mathrm{S}}^1\mathrm{P}\right|=2\mathrm{a} \\ \Rightarrow \left|\sqrt{{\left(24\right)}^2+{\left(7\right)}^2}-\sqrt{{\left(5\right)}^2+{\left(12\right)}^2}\right|=2\mathrm{a} \\ \Rightarrow \sqrt{625}-\sqrt{169}=2\mathrm{a} \\ \Rightarrow 2\mathrm{a}=12\Rightarrow \mathrm{a}=6 \\ and {\mathrm{SS}}^1=2\mathrm{ae}\Rightarrow \sqrt{{(24-5)}^2+{(7-12)}^2}=2\left(6\right) \left(\mathrm{e}\right) \\ \Rightarrow \sqrt{{\left(19\right)}^2+{\left(5\right)}^2}=12\mathrm{e} \\ \Rightarrow 12\mathrm{e}=\sqrt{386} \\ \Rightarrow \mathrm{e}=\frac{\sqrt{386}}{12} \end{gathered}$$