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The centre of a circle C is at the centre of the ellipse E: x^2 a^2 + y^2 b^2 =1, a b . Let C pass through the foci F₁ and F₂ of E such that the circle C and the ellipse E intersect at four points. Let P be one of these four points. If the area of the triangle PF ₁ ~F ₂ is 30 and the length of the major axis of E is 17 , then the distance between the foci of E is :

Options

  1. A26
  2. B13
  3. C12
  4. D13 2

Correct answer

B. 13

Step-by-step solution

aligned & 1 2 PF ₁ PF ₂=30 & PF ₁+ PF ₂=17 & PF ₁=12 PF ₂=5 & ~F ₁ ~F ₂=13 & option (2) aligned

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