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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

(a) `4//sqrt3`

B

(b) `2//sqrt3`

C

(c) `sqrt3`

D

(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

  • What is the eccentricity of the ellipse whose length of minor axis is equal to the distance between the two foci?

    A
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    B
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    C
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    D
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