Question

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

• A. $x^2-y^2=4$
• B. $x^2-y^2=8$
• C. $x^2-y^2=16$
• D. $x^2-y^2=32$

Answer 1

The correct option is D

$x^2-y^2=32$

Given that distance between foci, 2c =16
$c=8;e=\sqrt{2}$
$a=\frac{c}{e}=\frac{8}{\sqrt{2}}=4\sqrt{2}b=\sqrt{c^2-a^2}=\sqrt{32}=4\sqrt{2}$

The equation of the hyperbola is
$\frac{x^2}{32}-\frac{y^2}{32}=1\Rightarrow x^2-y^2=32$