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The equation of an ellipse with focus at (1, –1), directrix x – y – 3 = 0 and eccentricity ½ is

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The equation of an ellipse with focus at (1, –1), directrix x – y – 3 = 0 and eccentricity ½ is

(A) 7x2 + 2xy + 7y2 + 7 = 0

(B) 7x2 + 2xy + 7y2 – 10x + 10y + 7 = 0

(C) 7(x2 + y2) + 2xy + 10x – 10y + 7 = 0

(D) 7(x2 + y2) + 2xy – 10x – 10y + 7 = 0

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1 Answer

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Correct option: (B) 7x2 + 2xy + 7y2 – 10x + 10y + 7 = 0

Explanation: 

Here, we are given the focus,S (1, –1), directrix x – y – 3 = 0 and eccentricity ½

Let P(x, y) be any point, then according to definition of ellipse we have

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