Question

Find the equation to the hyperbola, the distance between whose foci is $16$ and whose eccentricity is $\sqrt{2}$.

• A. $x^2-y^2=32$
• B. $x^2-y^2=18$
• C. $x^2-y^2=64$
• D. $x^2-y^2=48$

Answer 1

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

Given eccentricity of the hyperbola is $\sqrt{2}$
Hence hyperbola is rectangular $a=b$
Also given distance between focii is 16. $\Rightarrow 2ae=16\Rightarrow a=4\sqrt{2}$
Hence required hyperbola is given by, $x^2-y^2=a^2=32$