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# Find the equations of the hyperbola satisfying the given conditions: Foci: $(0,\pm 13)$ and Conjugate axis of length $24$.

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Given Foci: $(0,\pm 13)$ and Conjugate axis of length $24$ $\rightarrow c = 13$ and $2b = 24 \rightarrow b = 12$
Since $a^2+b^2 = c^2 \rightarrow a = \sqrt{169-144} = \sqrt{25} = 5$
Therefore, the equation of the hyperbola is as follows: $\;\large\frac{y^2}{25}$$-\large\frac{x^2}{144}$$=1$
answered Apr 8, 2014