Question

Find the equation of the hyperbola satisfying the given condition :

vertices (± 2, 0), foci (± 3, 0)

Answer 1

The vertices of the hyperbola are \[\left( \pm 2, 0 \right)\] and the foci are  \[\left( \pm 3, 0 \right)\].

Thus, the value of  \[a = 2\] and \[ae = 3\] 

Now, using the relation \[b^2 = a^2 ( e^2 - 1)\], we get:

\[\Rightarrow b^2 = 9 - 4\]

\[ \Rightarrow b^2 = 5\]

Thus, the equation of the hyperbola is  \[\frac{x^2}{4} - \frac{y^2}{5} = 1\].