Home
Class 12
MATHS
The eccentricity of the hyperbola whose ...

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 :

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)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise (Numerical)|13 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Question Bank|25 Videos

Similar Questions

Explore conceptually related problems

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

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

Knowledge Check

  • The eccentricity of the hyperbola whose length of the latus reetum is equal to 8 and the length of its conjugate axis is equal to half of the distnce between its foci , is :

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

  • The eccentricity of an ellipse whose length of latus rectum is equal to distance between its foci, is

    A
    `2 sin 18^@`
    B
    `2 cos 36^@`
    C
    `sin 18^@`
    D
    `cos 36^@`

  • Length of latus rectum is half of minor axis

    A
    `sqrt(3)//2`
    B
    `1//4`
    C
    `1//2`
    D
    none

    • Similar Questions

    Explore conceptually related problems

    Find the equation of the hyperbola , the length of whose latus rectum is 4 and the eccentricity is 3.

    Find the equation of the hyperbola in which the length of conjugate axis is 5 and the distance between foci is 13.

    Find the eccentricity of the hyperbola,the length of whose conjugate axis is (3)/(4) of the length of transverse axis.

    The eccentricity of an ellipse, the length of whose minor axis is equal to the distance between the foci, is

    The length of the transverse axis and the conjugate axis of a hyperbola is 2a units and 2b units repectively. If the length of the latus rectum is 4 units of the conjugate axis is equal to one-third of the distance between the foci, then the eccentricity of the hyperbola is

    Home
    Profile