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If the latus rectum of a hyperbola x 2 a 2 - y 2 b 2 = 1 subtends an angle of 60 ° at the other focus, then the eccentricity of the hyperbola is

Options

  1. A2
  2. B3 + 1 2
  3. C2 3
  4. D3

Correct answer

D. 3

Step-by-step solution

Given that the latus rectum of a hyperbola x 2 a 2 - y 2 b 2 = 1 . . . . . . . . . . . . . . . . i subtends an angle of 60 ° at the other focus. As, foci are S a e , 0   &   S ' - a e , 0 End Points of latus rectum through S are given A a e ,   b 2 a ,   B a e ,   - b 2 a Given, A B subtends 60 0 at S ' Angle between S ' A with x -axis will be 30 0 . Slope of S ' A = m 1 = b 2 2 a 2 e = tan 30 ° ⇒ b 2 2 a 2 e = tan 30 0 = 1 3 ⇒ b 2 a 2 = 2 e 3 . . .

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