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

Length of Latus Rectum =

b² = 4a ------- (i)

As, Conjugate axis is equal to half of the distance between the foci,

2b = ae

Squaring the above mentioned equation,

4b² = a²e² -------- (ii)

b² = a² (1 - e²)

4a = a² (1 - e²)

4 = a (1 - e²)

-------- (iii)

Putting the value from equation (ii),

a = 20

b² = 4a = 4 × 20 = 80 {From equation (i)}

Hence, the eccentricity of hyperbola is .