Question

The distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2}$. Its equation is

• A. $x^2-y^2=32$
• B. $\frac{x^2}{4}-\frac{y^2}{9}=1$
• C. $2x-3y^2=7$
• D. none of these

Answer 1

The correct option is A $x^2-y^2=32$

Given

$2ae=16$ and $e=\sqrt{2}$

$ae=8$

$a=4\sqrt{2}$

And $e=\sqrt{1+\frac{b^2}{a^2}}$

Squaring both sides, we get

$e^2=1+\frac{b^2}{32}2=1+\frac{b^2}{32}Or,1=\frac{b^2}{32}{b}^2=32$

Equation of hyperbola is:

$x^2-y^2=32$

Hence, option A is correct.