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The equation of an ellipse whose focus is - 1 , 1 and whose directrix is x   -   y   +   3 = 0 and eccentricity is 1 2 is -

Options

  1. A7 x 2 + 2 x y + 7 y 2 + 10 x - 10 y + 7 = 0
  2. B7 x 2 - 2 x y + 7 y 2 - 10 x + 10 y + 7 = 0
  3. C7 x 2 - 2 x y + 7 y 2 - 10 x - 10 y - 7 = 0
  4. D7 x 2 - 2 x y + 7 y 2 + 10 x + 10 y - 7 = 0

Correct answer

A. 7 x 2 + 2 x y + 7 y 2 + 10 x - 10 y + 7 = 0

Step-by-step solution

Apply S P P M = e . (by definition) S P P M = 1 2 ⇒   4 S P 2 = P M 2 ⇒ 4 h + 1 2 + k - 1 2 = h - k + 3 2 2 ⇒   7 x 2 + 2 x y + 7 y 2 + 10 x - 10 y + 7 = 0

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