Complex Numbers And Quadratic Equations question 365
Question: The locus represented by $ |z-1|=|z+i| $ is [EAMCET 1991]
Options:
A) A circle of radius 1
B) An ellipse with foci at $ (1,0) $ and (0, - 1)
C) A straight line through the origin
D) A circle on the line joining $ (1,0),(0,1) $ as diameter
Show Answer
Answer:
Correct Answer: C
Solution:
$ |z-1|=|z+i| $
Þ $ |x-1+iy{{|}^{2}}=|x+i(y+1){{|}^{2}} $
Þ $ {{(x-1)}^{2}}+y^{2}=x^{2}+{{(y+1)}^{2}} $
Þ $ x+y=0 $ i.e., a straight line through the origin.
BETA
