(Solved): Find the standard form of the equation of the hyperbola satisfying the given conditions. Center: \( ...

Find the standard form of the equation of the hyperbola satisfying the given conditions. Center: \( (2,-4) \); focus: \( (9,-4) \); vertex: \( (8,-4) \) \[ \begin{array}{l} \frac{(x-8)^{2}}{36}-\frac{(y+4)^{2}}{13}=1 \\ \frac{(x-2)^{2}}{36}+\frac{(y+4)^{2}}{13}=1 \\ \frac{(x-2)^{2}}{13}-\frac{(y+4)^{2}}{36}=1 \\ \frac{(x-2)^{2}}{36}-\frac{(y+4)^{2}}{13}=1 \end{array} \]