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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 ______

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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 x^2-y^2=4 is

    A
    2
    B
    `2sqrt2`
    C
    `sqrt2`
    D
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  • The eccentricity of the hyperbola 2x = a(t + (1)/(t)), 2y = a(t-(1)/(t))

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    D
    `2sqrt(2)`

  • If e_1 is the eccentricity of the hyperbola (y^(2))/(b^(2)) - (x^(2))/(a^(2)) = 1 then e_(1) =

    A
    `sqrt(1+(a^(2))/(b^(2)))`
    B
    `sqrt(1-(a^(2))/(b^(2)))`
    C
    `sqrt(1+(b^(2))/(a^(2)))`
    D
    `sqrt(1-(b^(2))/(a^(2)))`

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