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Let a > 0, b > 0. Let a and  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 be the eccentricity and length of the latus rectum of its conjugate hyperbola. If e 2 = 1 1 1 4 l     a n d     ( e ' ) 2 = 1 1 8 l ' , then the value of 77a + 44b is equal to

Option 1 -

100

Option 2 -

110

Option 3 -

 120

Option 4 -

130

0 2 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    2 months ago
    Correct Option - 4


    Detailed Solution:

    x 2 a 2 − y 2 b 2 = 1

    e = 1 + b 2 a 2 e ' = 1 + a 2 b 2

    l = 2 b 2 a l ' = 2 a 2 b

    ( 1 + b 2 a 2 ) = 1 1 1 4 × 2 b 2 a ( 1 + a 2 b 2 ) = 1 1 8 × 2 a 2 b

    7 × { ( 7 b 4 ) 2 + b 2 } = 1 1 × b 2 × 7 b 4                 ⇒ a × 7 7 = 6 5

    65b2 = 44b3

    65 = b × 44

    ∴ 7 7 a + 4 4 b = 6 5 × 2 = 1 3 0

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Kindly go through the solution 

 

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