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# Find the equations of the hyperbola satisfying the given conditions: Vertices: $(0,\pm 5)$, Foci: $(0,\pm 8)$

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Given Vertices: $(0,\pm 5)$, Foci: $(0,\pm 8) \rightarrow a = 5, c = 8$
Since $a^2+b^2 = c^2 \rightarrow b = \sqrt{64-25} = \sqrt{39}$
Therefore, the equation of the hyperbola is as follows: $\;\large\frac{y^2}{25}$$-\large\frac{x^2}{39}$$=1$
edited Apr 8, 2014