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 :

Options

A. `(4)/(3)`
B. `(4)/(sqrt(3))`
C. `(2)/(sqrt(3))`
D. `sqrt(3)`

Answer

C

Explanation

Let the hyperbola be `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` and `e` be its eccentricity. It is given that `(2b^(2))/(a)=8` and `2b=ae`
Now, `2b=aeimplies(b)/(a)=(e)/(2)implies1+(b^(2))/(a^(2))=1+(e^(2))/(4)impliese^(2)=1+(e^(2))/(4)`
`implies(3)/(4)e^(2)=1impliese=(2)/(sqrt(3))`