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Let L L ' be the latus rectum through the focus S of a hyperbola and A be the farther vertex of the conic. If Δ   A   L L ' is equilateral then its eccentricity is

Options

  1. A3
  2. B3 + 1
  3. C3 + 1 2
  4. D1 + 1 3

Correct answer

D. 1 + 1 3

Step-by-step solution

A M = a + a e M L ' = b 2 a θ = 3 0 ° ⇒   b 2 a a + a e = 1 3 ⇒ b 2 a 2 = e + 1 3 ⇒     e 2 - 1 = e + 1 3 ⇒   e - 1 = 1 3 ⇒   e = 1 + 1 3

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