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प्रश्न
Find the equation of the hyperbola satisfying the given condition :
vertices (0, ± 3), foci (0, ± 5)
उत्तर
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 \[- \frac{x^2}{16} + \frac{y^2}{9} = 1\].
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