Question

Find the equation of the hyperbola satisfying the given condition :

 vertices (0, ± 5), foci (0, ± 8)

Answer 1

The vertices of the hyperbola are \[\left( 0, \pm 5 \right)\] and the foci are  \[\left( 0, \pm 8 \right)\] Thus, the value of \[a = 5\] and \[ae = 8\]

Now, using the relation 

\[b^2 = a^2 ( e^2 - 1)\], we get:

\[\Rightarrow b^2 = 64 - 25\]

\[ \Rightarrow b^2 = 39\]

Thus, the equation of the hyperbola is  \[- \frac{x^2}{39} + \frac{y^2}{25} = 1\].