Let a > 0 , b > 0 . Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola x 2 a 2 - y 2 b 2 = 1 . Let e ' and l ' respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If e 2 = 11 14 l and e ' 2 = 11 8 l ' , then the value of 77 a + 44 b is equal to

Step-by-step solution

By using eccentricty formula we get, e = 1 + b 2 a 2 , l = 2 b 2 a Given e 2 = 11 14 l So, 1 + b 2 a 2 = 11 14 · 2 b 2 a a 2 + b 2 a 2 = 11 7 · b 2 a           ⋯ 1 Also e ' = 1 + a 2   b 2 , l ' = 2 a 2   b Given e ' 2 = 11 8 l ' 1 + a 2 b 2 = 11 8 · 2 a 2 b a 2 + b 2 b 2 = 11 4 · a 2 b           ⋯ 2 Now equation 1 ÷ equation 2 we get, b 2 a 2 = 4 7 · b 3 a 3 ∴ 7 a = 4 b       &