UPSEE 2017 Solved Paper

Given,
Coordinate of focus ≡(−1,1)
Equation of directrix : x−y+3=0
Eccentricity =

1

2

We know that, an ellipse is the locus of the point which moves in the plane so that ratio of its distance from a focus and a directrix is equal to eccentricity of the ellipse.
∴ From definition of the ellipse,

PS

PM

=e
⇒

√(x+1)2+(y−1)2

x−y+3 √2

=

1

2

⇒√(x+1)2+(y−1)2=

1

2

x−y+3

√2

By squaring both side, we get
(x+1)2+(y−1)2=

1

8

(x−y+3)2