The difference between the focal dintences of any point on the hyperbola $\large\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=$$1 is 24 and the eccentricity is 2. Then the equation of the hyperbola is $\begin{array}{1 1}(1)\frac{x^{2}}{144}-\frac{y^{2}}{432}=1&(2)\frac{x^{2}}{432}-\frac{y^{2}}{144}=1\\(3)\frac{x^{2}}{12}-\frac{y^{2}}{12\sqrt{3}}=1&(4)\frac{x^{2}}{12\sqrt{3}}-\frac{y^{2}}{12}=1\end{array}$ 1 Answer SP-S'P =2a 24=2a a=12 Eccentricity e= 2 b^2= a^2(e^2-1) \qquad= 12^2(4-1) \qquad= 144 \times 3 b^2= 432 Equation of the hyperbola is \large\frac{x^{2}}{144}-\frac{y^{2}}{432}$$=1$
Hence 1 is the correct answer.