If the distance between the foci of a hyperbola is `16` and its eccentricity is `sqrt(2)` , then obtain its equation.

Explanation

Distance between the foci of the hyperbola,

`2ae =16`

Eccentricity of the hyerbola, `e = sqrt2`

`:. (2ae)/e = 16/sqrt2`

`a = 8/sqrt2 = 4sqrt2`

Now,

`e^2 = 1+ b^2/a^2`

`=>sqrt2^2 = 1 + b^2/(4sqrt2)^2`

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