Verified Solution • 2025–26 Session moderate

QJEEM19Ma54b6: JEE Main 2019 Mathematics - Class 11 JEEM19Ma54b6 Solution: If a hyperbola has length of its conjugate axis equal to 5 and…

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :

Multiple Choice Options

  • A 136{{13} \over 6}
  • B 2
  • C 1312{{13} \over 12}
  • D 138{{13} \over 8}

Step-by-Step Verified Solution

2b = 5 and 2ae = 13

b2 = a2(e2 −- 1) ⇒\Rightarrow    254{{25} \over 4} = 1694{{169} \over 4} −- a2

⇒\Rightarrow   a == 6 ⇒\Rightarrow   e == 1312{{13} \over {12}}

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