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Question
Find the equation of the hyperbola satisfying the given condition :
foci (0, ± 13), conjugate axis = 24
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Solution
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
\[\Rightarrow a^2 = 169 - 144\]
\[ \Rightarrow a^2 = 25\]
Thus, the equation of the hyperbola is \[- \frac{x^2}{144} + \frac{y^2}{25} = 1\] .
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