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CGP EDU Academic Team
Published on: August 14, 2026
The equation to the ellipse, whose focus is the point (–1, 1), whose directrix is the straight line x – y + 3 = 0, and whose eccentricity is 
is -
Text Solution
Verified by ExpertsThe correct answer is:
A
If P(x, y) be any point on the ellipse, S be its focus, and PN be the perpendicular from P on directrix, then by definition of an ellipse
PS 2 = e 2 PN 2 , hence
(x + 1) 2 + (y – 1) 2 = 
= 
[As focus is (–1, 1) and directrix is x – y + 3 = 0]
⇒ 8(x 2 + y 2 + 2x – 2y + 2) = x 2 + y 2 + 9 – 2xy
+ 6x – 6y
7x 2 + 2xy + 7y 2 + 10x – 10y + 7 = 0.
Hence is the correct answer.
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