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The eccentricity of the hyperbola |sqrt(...

The eccentricity of the hyperbola `|sqrt((x-3)^2+(y-2)^2)-sqrt((x+1)^2+(y+1)^2)|=1` is ______

Text Solution

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The correct Answer is:
5
For the given equation of the hyperbola, the foci are S(3, 2) and `S'(-1,-1)`.
Using the definition of hyperbola, `|SP-S'P|=2a` we have `SS'=5 and 2a=1`.
Hence, eccentricity is, `e=(SS')/(2a)=5`.
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Knowledge Check

  • The eccentricity of the hyperbola (y^(2))/(9)-(x^(2))/(25)=1 is …………………

    A
    `(34)/(3)`
    B
    `(5)/(3)`
    C
    `(sqrt34)/(3)`
    D
    `(sqrt34)/(5)`

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    A
    `(16)/(25)`
    B
    1
    C
    Greater than 1
    D
    Less than `1/2`

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