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JEE Main 2019 · 11 Jan · Shift II

JEE Main 2019 Mathematics question on Conic Sections

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
  1. A.
    1312\dfrac{13}{12}
  2. B.
    22
  3. C.
    138\dfrac{13}{8}
  4. D.
    136\dfrac{13}{6}
Show answer and solution

Correct option: A

Solution

2b = 5, so b = 5/2. Distance between foci = 2ae = 13, so ae = 13/2. Using b² = a²(e²-1): (5/2)² = (13/2)² - a², giving a² = 169/4 - 25/4 = 144/4 = 36, so a = 6. Therefore e = (13/2)/6 = 13/12.

[JEE Main 2019 · 11 Jan · Shift II]

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