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प्रश्न
Find the equation of the hyperbola whose vertices are at (0 ± 7) and foci at \[\left( 0, \pm \frac{28}{3} \right)\] .
उत्तर
The Vertices of the hyperbola are \[\left( 0, \pm 7 \right)\].
∴ \[b = 7\]
The foci is \[\left( 0, \pm \frac{28}{3} \right)\].
∴ \[be = \frac{28}{3}\]
Also,\[ a^2 = b^2 \left( e^2 - 1 \right)\]
\[ \Rightarrow a^2 = \left( \frac{28}{3} \right)^2 - 49\]
\[ \Rightarrow a^2 = \frac{343}{9}\]
Therefore, the equation of the hyperbola is \[- \frac{9 x^2}{343} + \frac{y^2}{49} = 1\].
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