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If P Q is a double ordinate of the hyper...

If `P Q` is a double ordinate of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` such that `O P Q` is an equilateral triangle, `O` being the center of the hyperbola, then find the range of the eccentricity `e` of the hyperbola.

A

`e=(2)/sqrt(3)`

B

`e=sqrt(3)/(2)`

C

`egt(2)/sqrt(3)`

D

`1ltelt(2)/sqrt(3)`

Text Solution

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The correct Answer is:
c
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If PQ is a double ordinate of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 such that OPQ is an equilateral triangle,O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.

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Knowledge Check

  • If PQ is a double ordinate of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 such that OPQ is an equilateral triangle, O being the centre of the hyperbola, then the eccentricity e of the hyperbola satisfies

    A
    `1ltelt(2)/(sqrt(3))`
    B
    `e=(2)/(sqrt(3))`
    C
    `e=sqrt(3)/(2)`
    D
    `egt(2)/(sqrt(3))`

  • If PQ is a double ordinate of the hyperbola such that OPQ is an equilateral triangle, being the centre of the hyperbola, then eccentricity e of the hyperbola satisfies

    A
    `e=(2)/sqrt(3)`
    B
    `e=sqrt(3)/(2)`
    C
    `egt(2)/sqrt(3)`
    D
    `1ltelt(2)/sqrt(3)`

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

    A
    `sqrt2`
    B
    ` (1)/(sqrt2)`
    C
    `2`
    D
    `1+sqrt2`

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