# The equation of the ellipse whose focus is (1,0) and the directrix is x+ y+1=0 and eccentricity is equal to 1/√2 is

A

(x1)2+y2=(x+y+1)2

B

2(x1)2+Y2=(x+y+1)2

C

4{(x1)2+y2}=(x+y+1)2

D

none of these

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## Let S(1,0) be the focus and ZZ' be the directrix let P(x,y) be any point on the ellipse and PM be perpendicular from P on directrix . Then by definition , we have . SP=ePM, where e=1/√2 ⇒SP2=e2PM2 ⇒(x−1)2+(y−0)2=(1√2)2{x+y+1√1+1}2 ⇒4{(x−1)2+y2}=(x+y+1)2

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Updated on:21/07/2023

### Knowledge Check

• Question 1 - Select One

## The equation of the ellipse whose focus is (1,-1), directrix x−y−3=0 and eccentricity equals 12 is :

A7x2+2xy+7y210x+10y+7=0
B7x2+2xy+7y2+7=0
C7x2+2xy+7y2+10x10y7=0
D7x2+2xy+7y2+10x10y7=0
• Question 2 - Select One

## If question of the ellipse whose focus is (1,−1), then directrix the line x−y−3=0 and eccentricity 12 is

A7x2+2xy+7y210x+10y+7=0
B7x2+2xy+7y2+7=0
C7x2+2xy+7y2+10x10y7=0
Dnone of these
• Question 3 - Select One

## The equation of an ellipse whose focus is (−1,1), directrix is x−y+3=0 and eccentricity is 12, is given by

A7x2+2xy+7y2+10x10y+7=0
B7x22xy+7y210x+19y+7=0
C7x22xy+7y210x10y7=0
D7x22xy+7y2+10x10y7=0

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