wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Locus of the point z satisfying the equation |iz1|+|zi|=2 is-

A
straight line segment
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
a circle
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
an ellipse
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a pair of straight line
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A straight line segment
z=x+iy
|iz1|+|zi|=2
|i(x+iy)1|+|x+iyi|=2
|ix(y1)|+|x+i(y1)=2
(y1)2+(x)2+x2+(y1)2=2 ….(1)
Also, x2+(y+1)2x2+(y1)2=4y ….(2)
Divide equation (2) by (1) we get
x2+(y+1)2x2+(y1)2=2y ….(3)
Adding (1) and (3) gives
2x2+(y+1)2=2+2y
x2+(y+1)2=(y+1)2
x=0 which is y-axis
A straight line (Answer).

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Modulus
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon