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Let the equations of two ellipses be E₁: x^2 3 + y^2 2 =1 and E₂: x^2 16 + y^2 b^2 =1 , If the product of their eccentricities is 1 2 , then the length of the minor axis of ellipse E₂ is :

Options

  1. A8
  2. B9
  3. C4
  4. D2

Correct answer

C. 4

Step-by-step solution

Given equations of ellipses aligned & E ₁: x^2 3 + y^2 2 =1 & e₁= 1- 2 3 = 1 3 & and E ₂: x^2 16 + y^2 b^2 =1 & e₂= 1-b^2 16 = 16-b^2 4 & Also, given e₁ e₂= 1 2 & 1 3 16-b^2 4 = 1 2 16-b^2=12 & b^2=4 & Length of minor axis of & E ₂=2 b=2 2=4 aligned

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