Verified Solution • 2025–26 Session moderate

QJEEM16Ma8b86: JEE Main 2016 Mathematics - Class 11 JEEM16Ma8b86 Solution: A hyperbola whose transverse axis is along the major axis of…

A hyperbola whose transverse axis is along the major axis of the conic, x23+y24=4{{{x^2}} \over 3} + {{{y^2}} \over 4} = 4 and has vertices at the foci of this conic. If the eccentricity of the hyperbola is 32,{3 \over 2}, then which of the following points does NOT lie on it?

Multiple Choice Options

  • A (0, 2)
  • B (5,22)\left( {\sqrt 5 ,2\sqrt 2 } \right)
  • C (10,23)\left( {\sqrt {10} ,2\sqrt 3 } \right)
  • D (5,23)\left( {5,2\sqrt 3 } \right)

Step-by-Step Verified Solution

x212+y216{{{x^2}} \over {12}} + {{{y^2}} \over {16}} = 1

e = 1−1216\sqrt {1 - {{12} \over {16}}} = 12{1 \over 2}

Foci (0, 2)   &   (0, −- 2)

So, transverse axis of hyperbola

= 2b = 4

⇒\Rightarrow b = 2 & a2 = 12 (e2 −- 1)

⇒\Rightarrow    a2 = 4 (94−1)\left( {{9 \over 4} - 1} \right)

⇒\Rightarrow    a2 = 5

∴\therefore     It's equation is x25−y24{{{x^2}} \over 5} - {{{y^2}} \over 4} = −- 1

The point (5, 2 3\sqrt 3 ) does not satisfy the above equation.

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