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  • . The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity is A. 7x^2 + 2xy + 7y^2 – 10x + 10y + 7 = 0 B. 7x^2 + 2xy + 7y^2 + 7 = 0 C. 7x^2 + 2xy + 7y^2 + 10x – 10y – 7 = 0 D. none

The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity 1/2 is
A. 7x2 + 2xy + 7y2 – 10x + 10y + 7 = 0
B. 7x2 + 2xy + 7y2 + 7 = 0
C. 7x2 + 2xy + 7y2 + 10x – 10y – 7 = 0
D. none

Answers (1)

Option (a) is correct.

Given that focus of the ellipse is S(1,-1)and the equation of directrix is x-y-3=0  

Also, e=1/2 

From definition of ellipse, for any point P (x,y) on the ellipse, we have SP=ePM, where

 M is foot of the perpendicular from point P to the directrix. 

\sqrt{(x-1)^{2}+(y+1)^{2}}=\frac{1}{2}\frac{\left | x-y-3 \right |}{\sqrt{2}}

7x2+7y2+2xy-10x+10y+7=0

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