Question

Find the equation of the hyperbola satisfying the given condition :

 foci (± \[3\sqrt{5}\] 0), the latus-rectum = 8

Answer 1

 The foci of  the hyperbola  are \[\left( \pm 5, 0 \right)\] and the transverse axis is 8.
Thus, the value of  \[ae = 5\] and 2a = 8.

\[\Rightarrow a = 4\]

Now, using the relation

\[b^2 = a^2 ( e^2 - 1)\], we get:

\[\Rightarrow  b^2  = 25 - 16\] 

 

\[ \Rightarrow  b^2  = 9\] 

Thus, the equation of the hyperbola is \[\frac{x^2}{16} - \frac{y^2}{9} = 1\].