# Find the equations of the hyperbola satisfying the given conditions: Vertices : $(\pm 7 )$, $e = \large\frac{4}{3}$

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Vertices : $(\pm 7 ) \rightarrow a = 7$
Given $e = \large\frac{4}{3}$$\rightarrow \large\frac{4}{3}$$=\large\frac{c}{7}$$\rightarrow c =\large\frac{28}{3} Since a^2+b^2 = c^2 \rightarrow b = \sqrt{ (\large\frac{28}{3})^2 \normalsize- \normalsize 49 \normalsize}$$ = \large\frac{\sqrt{343}}{3}$
Therefore, the equation of the hyperbola is as follows: $\;\large\frac{x^2}{49}$$-9\large\frac{y^2}{343}$$=1$
edited Apr 8, 2014