Question

If the distance between the foci of a hyperbola is 16 and its eccentricity is $\sqrt{2}$ , then obtain the equation of the hyperbola.

Answer 1

Let $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

$c=\sqrt{2}=1$

$a=b$

$2ae=16$

$\Rightarrow a=4\sqrt{2}$

$\Rightarrow b=4\sqrt{2}$

$\therefore x^2-y^2=32$.