Write the equation of the hyperbola of eccentricity `sqrt(2)` if it is known that the distance between its foci is 16.

Explanation

Given `e=sqrt2` for hyperbola and distance between foci is 16 and we know distance between foci =`2C=16`

[C=8]

and C= `sqrt(a^2+b^2)=8 `……….(1)
and `e=sqrt2`

We know
`a=C/B=8/sqrt2=4sqrt2`

`[a=4sqrt2]`

and from equation (1) we get

`sqrt(a^2+b^2)=8`

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