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An ellipse has foci 4,2 , 2,2 and it passes through the point P 2,4 . The eccentricity of the ellipse is

Options

  1. At a n π 10
  2. Bt a n π 12
  3. Ct a n π 6
  4. Dt a n π 8

Correct answer

D. t a n π 8

Step-by-step solution

Let, 4 , 2 = S 1 and 2 , 2 = S 2 and eccentricity of ellipse is e then S 1 S 2 = 2 a e and P S 1 + P S 2 = 2 a (where 2 a is length of major axis) ⇒ e = S 1 S 2 P S 1 + P S 2 = 2 2 2 + 2 ⇒ e = 1 2 + 1 = 2 - 1 = t a n π 8

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