If the angle between the asymptotes of hyperbola a 2 x 2 − b 2 y 2 = 1 is 3 π . Then the eccentricity of conjugate hyperbola is

Question

If the angle between the asymptotes of hyperbola a 2 x 2 ​ − b 2 y 2 ​ = 1 is 3 π ​ . Then the eccentricity of conjugate hyperbola is

TestHub · Accepted Answer

2 tan − 1 ( a b ​ ) = 3 π ​ a b ​ = 3 ​ 1 ​ e 2 = 1 + 3 1 ​ = 3 4 ​ e ′2 1 ​ + e 2 1 ​ = 1 ⇒ e ′ 2 1 ​ + 4 3 ​ = 1 ⇒ e ′ 2 1 ​ = 4 1 ​ ⇒ e ′ = 2

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