Question

Find the equation of the hyperbola satisfying the given condition :

 foci (0, ± 13), conjugate axis = 24

Answer 1

The foci of the hyperbola are \[\left( 0, \pm 13 \right)\]  and the conjugate axis is 24.
Thus, the value of \[ae = 13\] and 2b = 24.
⇒ b = 12

Now, using the relation 

\[b^2 = a^2 ( e^2 - 1)\], we get:

\[\Rightarrow a^2 = 169 - 144\]

\[ \Rightarrow a^2 = 25\]

Thus, the equation of the hyperbola is \[- \frac{x^2}{144} + \frac{y^2}{25} = 1\] .