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JEE Main20249 Apr 2024Evening ShiftMathematicsHyperbolaActual

Let the foci of a hyperbola H coincide with the foci of the ellipse E: (x-1)^2 100 + (y-1)^2 75 =1 and the eccentricity of the hyperbola H be the reciprocal of the eccentricity of the ellipse E . If the length of the transverse axis of H is and the length of its conjugate axis is , then 3 ^2+2 ^2 is equal to

Options

  1. A237
  2. B242
  3. C205
  4. D225

Correct answer

D. 225

Step-by-step solution

aligned & e ₁= 1- 75 100 = 5 10 = 1 2 & e ₂=2 & ~F ₁(6,1), F ₂(-4,1) & 2 ae ₂=10 a = 5 2 2 a =5 & =5 & 4=1+ b ^2 a ^2 b ^2=3 a ^2 & ~b = 3 5 2 & =5 3 & 3 ^2+2 ^2=3 25+2 25 3 & =225 aligned

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