If P Q is a double ordinate of the hyperbola x^2 a^2 - y^2 b^2 =1 such that O P Q is an equilateral triangle, O bing the centre of the hyperbola, then the eccentricity e of the hyperbola satisfies.

Step-by-step solution

Let the hyperbola be x^2 a^2 - y^2 b^2 =1 and any double ordinate P Q be (a ₁ b ), (a ₁-b ) and O is centre (0,0) . O P^ Q being equilateral. 30^ = b a array lr & 3 b^2 a^2 = cosce ^2 & 3 (e^2-1 )= cosce ^2 array Now, cosec ^2 1 3 (e^2-1 ) 1 e^2 4 3 array ll & e 2 / 3 array