JEE Advanced 2021 Full Test 2 Paper 1

|z−1|+|z−i|=4 represents ellipse with foci (1,0) and (0,−1) and length of major axis =4. Centre of ellipse is (

1

2

,−

1

2

) and (

1−i

2

)
2a=4,2ae=√2⇒e=

1

2√2

From b2=a2(1−e2), we get b=√

7

2

Now |2z−1+i|=√14
⇒|z−

1

2

+

i

2

|=√

7

2

⇒|z−(

1−i

2

)|=√

7

2

represents a circle having centre at

1−i

2

and radius =√

7

2

.
Since radius of circle = minor axis of ellipse.
Hence number of solution of given equation =2.