The eccentricity of the hyperbola whose length of the latus rectum is equal to 8

• Coordinate Geometry

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

1. 4/√3
2. 2/√3
3. √3
4. 4/3

Solution

Length of conjugate axis = half the distance between foci

2b = ½(2ae)

b = ae/2

Length of latus rectum = 2b²/a = 8

b² = 4a

a²e²/4 = 4a

ae² = 16

a²(e² - 1) = 4a

ae² - a = 4

16 - a = 4

a = 12

ae² = 16

e² = 4/3

e = 2/√3

The correct option is B.