Home
Class 12
MATHS
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)/(3)`

B

`(4)/(sqrt(3))`

C

`(2)/(sqrt(3))`

D

`sqrt(3)`

Text Solution

Verified by Experts

We have, `(2b^(2))/(a)=8 and 2b=ae`
` rArr b^(2)=4a and 2b=ae`
consider, `2b=ae`
`rArr 4b^(2)=a^(2)e^(2)`
`rArr 4a^(2)(e^(2)-1)=a^(2)e^(2)`
`rArr 4e^(2)-4=e^(2) " "[ because a ne 0]`
` rArr 3e^(2)=4`
`rArr e=(2)/(sqrt(3)) " "[because e gt 0]`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

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)

find the equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13.

Find the equation of the ellispe whose latus rectum is 5 and e = 2/3

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is

Find the eccentricity of the hyperbola with foci on the x-axis if the length of its conjugate axis is (3/4)^("th") of the length of its tranverse axis.

If S_1a n dS_2 are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_3a n dS_4 are the foci of the conjugate hyperbola, then the area of quadrilateral S_1S_3S_2S_4 is 24 (b) 26 (c) 22 (d) none of these

Consider an ellipse x^2/a^2+y^2/b^2=1 Let a hyperbola is having its vertices at the extremities of minor axis of an ellipse and length of major axis of an ellipse is equal to the distance between the foci of hyperbola. Let e_1 and e_2 be the eccentricities of an ellipse and hyperbola respectively. Again let A be the area of the quadrilateral formed by joining all the foci and A, be the area of the quadrilateral formed by all the directrices. The relation between e_1 and e_2 is given by