Question

Find the equation of the hyperbola satisfying the given condition :

vertices (0, ± 3), foci (0, ± 5)

Answer 1

The vertices of the hyperbola are \[\left( 0, \pm 3 \right)\] and the foci are \[\left( 0, \pm 5 \right)\].

Thus, the value of  \[a = 3\] and \[ae = 5\].

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

\[\Rightarrow b^2 = 25 - 9\]

\[ \Rightarrow b^2 = 16\]

Thus, the equation of the hyperbola is   \[- \frac{x^2}{16} + \frac{y^2}{9} = 1\].