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The eccentricity of the hyperbola whose ...

The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

A

`4//sqrt3`

B

`2//sqrt3`

C

`sqrt3`

D

`4//3`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `2b=(1)/(2)(2ae)rArr b = (ae)/(2)`
Now `b^(2)=a^(2)(e^(2)-1)`
`rArr" "a^(2)(e^(2)-1)=(a^(2)e^(2))/(4)rArr3e^(2)=4rArre=(2)/(sqrt3)`
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The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is : (1) 4/3 (2) 4/(sqrt(3)) (3) 2/(sqrt(3)) (4) sqrt(3)

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Knowledge Check

  • The eccentricity of the yhyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

    A
    `4/3`
    B
    `4/sqrt3`
    C
    `2/sqrt3`
    D
    `3/2`

  • If the length of the latus rectum is half the length of the conjucate axes of a hyperbola then its eccentricity is:

    A
    `sqrt(5)`
    B
    `(sqrt(5))/(2)`
    C
    `(sqrt(5))/(sqrt(2))`
    D
    `2sqrt(5)`

  • Equation of the hyperbola, whose eccentricity 3/2 and foci at (pm2,0) is . . .

    A
    `(x^(2))/(4)-(y^(2))/(5)=4/9`
    B
    `(x^(2))/(9)-(y^(2))/(9)=4/9`
    C
    `(x^(2))/(4)-(y^(2))/(9)=1`
    D
    None of these

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