The difference between the focal dintences of any point on the hyperbola $\large\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=$$1$ is $24$ and the eccentricity is $2$. Then the equation of the hyperbola is

Question

\[\begin{array}{1 1}(1)\frac{x^{2}}{144}-\frac{y^{2}}{432}=1&(2)\frac{x^{2}}{432}-\frac{y^{2}}{144}=1\\(3)\frac{x^{2}}{12}-\frac{y^{2}}{12\sqrt{3}}=1&(4)\frac{x^{2}}{12\sqrt{3}}-\frac{y^{2}}{12}=1\end{array}\]