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The tangents at the extremities of the latus rectum of the ellipse 3 x 2 + 4 y 2 = 12 form a rhombus P Q R S . Area (in sq. units) of the rhombus P Q R S outside the ellipse is equal to

Options

  1. A8 - 2 3 π
  2. B12 - 2 3 π
  3. C14 - π
  4. D16 - 2 3 π

Correct answer

D. 16 - 2 3 π

Step-by-step solution

One of the end of latus rectum is 1 , 3 2 Tangent at 1 , 3 2 is x + 2 y = 4 Area of rhombus = 4 1 2 ⋅ 4 ⋅ 2 = 16 Hence, the required area = 16 - 2 3 π sq. units

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