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Find the equation of the hyperbola the distance between whose foci is 16, whose eccentricity is `root()()2` and whose axis is along the x- axis with the origin as its centre .

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Knowledge Check

  • The equation of the hyperbola, whose foci are (6, 4) and (-4, 4) and eccentricity is 2, is

    A
    `12(x -1)^(2) - 4(y-4)^(2) = 75`
    B
    `12(x+1)^(2) -4(y+4)^(2) = 75`
    C
    `4(x - 1)^(2) - 1( y- 4)^(2) = 75`
    D
    `4(x + 1)^(2) - 12(y + 4)^(2) = 75`

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    The distance between the foci of hyperbola is 16 and its eccentricity is sqrt(2) . Its equation is

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