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The foci of the ellipse x^2 16 + y^2 b^2 =1 and the hyperbola x^2 144 - y^2 81 = 1 25 coincide. Then the value of b^2 is

Options

  1. A9
  2. B1
  3. C5
  4. D7

Correct answer

D. 7

Step-by-step solution

x^2 144 - y^2 81 = 1 25 a = 144 25 , ~b = 81 25 , e = 1+ 81 144 = 15 12 = 5 4 Foci =(3,0) , focus of ellipse =(3,0) e = 3 4 b^2=16 (1- 9 16 )=7

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