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$The equation of the ellipse having focus (1, - 1), directrix x - y - 3 = 0 and eccentricity 1 / 2 is$

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7x2+2xy+7y2−10x+10y+7=0

7x2+2xy+7y2+7=0

7x2+2xy+7y2+10x−10y−7=0

None of these

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detailed solution

Correct option is A

Let P(x,y) be any point on the ellipse. Then by definition, SP=ePM (where S is the focus and PM is the distance of P from the directrix). So (x−1)2+(y+1)2=12x−y−32⇒ (x−1)2+(y+1)2=18(x−y−3)2⇒ 7x2+2xy+7y2−10x+10y+7=0

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The equation of the ellipse having focus (1,−1), directrix x−y−3=0 and eccentricity 1/2 is

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$The equation of the ellipse having focus (1, - 1), directrix x - y - 3 = 0 and eccentricity 1 / 2 is$