Question

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

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

Answer 1

The correct option is D

$x^2-y^2=32$

$\text{The distance between the foci is 2ae}$

$\therefore 2ae=16$

$\Rightarrow ae=8$

$e=\sqrt{2}$

$\therefore a\sqrt{2}=8$

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

$Also,b^2=a^2(e^2-1)$

$\Rightarrow b^2=32(2-1)$

$\Rightarrow b^2=32$

$\text{Standard form of the hyperbola is given below :}$

$\frac{x^2}{32}-\frac{y^2}{32}=1$

$x^2-y^2=32$