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JEE Main20258 Apr 2025Evening ShiftMathematicsEllipseActual

Let the ellipse 3 x^2+ py ^2=4 pass through the centre C of the circle x^2+y^2-2 x-4 y-11=0 of radius r . Let f₁, f₂ be the focal distances of the point C on the ellipse. Then 6 f₁ f₂-r is equal to

Options

  1. A74
  2. B68
  3. C70
  4. D78

Correct answer

C. 70

Step-by-step solution

E : x ^2 4 / 3 + y ^2 4 / P =1 Centre of circle ( 1,2 ), radius aligned & r = 1+4+11 & r =4 aligned E pass from centre (1,2) 3 4 + P =1 P = 1 4 vertical ellipse aligned & e = 1- 4 / 3 16 = 1- 1 12 = 11 12 & Focal distance of C ( h , k ) & = b ek & F ₁=4+ 11 12 2 & ~F ₂=4- 11 12 2 & ~F ₁ ~F ₂=16- 11 3 = 37 3 & 6 ~F ₁ ~F ₂- r =74-4=70 aligned

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