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:

length of latus rectum=8
Given
So, 2b²/a=8
Length of conjugate axis = Half of distance between focii
So, 2b=ae
∴e=2b/a
2b/a × b=8
e × b=8; b=8/e
a=2b/e = 16/e²
e=√(1+b²/a²) = √(1+(64/e²)/(16/e²)⁴) = √(1+64e²/16e⁴)
4e²=4+e²
3e²=4
e²=4/3
e=2√3