The distance between the foci of a hyperbola is 16 and its eccentricity 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`

Explanation

The foci of the hyperbola `(a e, 0)` and `(-a e, 0)`.

Distance between the foci ` =sqrt{(a e-(-a e)^{2}+0^{2}} `

`=sqrt{(2 a e)^{2}} `

`=2 a e`

Distance between the foci is 16 and eccentricity of the hyperbola is `sqrt{2}`.

`therefore 2 a e=16`

`Rightarrow 2 sqrt{2} a=16`

`Rightarrow a=4 sqrt{2}` Now, `b^{2}=a^{2}(e^{2}-1)`

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