Question

Find the equation of the hyperbola whose vertices are at (0 ± 7) and foci at \[\left( 0, \pm \frac{28}{3} \right)\] . 

Answer 1

 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 \[- \frac{9 x^2}{343} + \frac{y^2}{49} = 1\].