The eccentricity of the hyperbola whose length of the latus rectum

• 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. √3
3. 4/3
4. 2/√3

Answer

Length of conjugate axis = half the distance between foci

2b = ½(2ae)

b = ae/2

Length of latus rectum = 2b²/a = 8

b² = 4a

ae² = 16

a = 12

The correct option is D.