Verified Solution • 2025–26 Session moderate

QJEEM16Maf7f0: JEE Main 2016 Mathematics - Class 11 JEEM16Maf7f0 Solution: Let a and b respectively be the semitransverse and…

Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation 9e2 − 18e + 5 = 0. If S(5, 0) is a focus and 5x = 9 is the corresponding directrix of this hyperbola, then a2 − b2 is equal to :

Multiple Choice Options

  • A 7
  • B − 7
  • C 5
  • D − 5

Step-by-Step Verified Solution

As  S(5, 0)   is the focus.

∴   ae = 5          . . . (1)

As  5x = 9

∴   x = 95 is the directrix

As we know directrix = ae

∴   ae=95           . . . .(2)

Solving (1) and (2), we get

a = 3 and e = 53

As we know,

b2 = a2 (e2 − 1) = 9(259−1) = 16

∴   a2 − b2 = 9 − 16 = − 7

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