) one focus is (-1, 1), directrix is x-y+3-0 and eccentricity is 2

1.	) one focus is (-1, 1), directrix is x-y+3-0 and eccentricity is 2
Answer» The focus is (-1,1). Directrix is x-y+3=0 and e =1/2. Let P(x₁,y₁) be any point on the ellipse, then SP² = e²PM² where PM is perpendicular distance from x-y+3=0 (x₁+1)² + (y₁-1)² = 1/4 [(x₁-y₁+3)/√(1+1)]² 8(x₁+1)² +8 (y₁-1)² = (x₁-y₁+3)² 7x₁²+2x₁y₁+7y₁²+10x₁-10y₁+7=0 Locus of (x₁,y₁) i.e., the equation of the required ellipse is 7x²+2xy+7y+10x-10y+7=0

Answer»

The focus is (-1,1).

Directrix is x-y+3=0 and e =1/2.

Let P(x₁,y₁) be any point on the ellipse, then SP² = e²PM² where PM is perpendicular distance from x-y+3=0

(x₁+1)² + (y₁-1)² = 1/4 [(x₁-y₁+3)/√(1+1)]²

8(x₁+1)² +8 (y₁-1)² = (x₁-y₁+3)²

7x₁²+2x₁y₁+7y₁²+10x₁-10y₁+7=0

Locus of (x₁,y₁) i.e., the equation of the required ellipse is

7x²+2xy+7y+10x-10y+7=0

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