A) \[|z-1|\,=\,|z-2|\]
B) \[|z-1|=|z-2|=|z-i|\]
C) \[|z-1|-|z-2|=2a\]
D) \[|z-1{{|}^{2}}+|z-2{{|}^{2}}=4\]
Correct Answer: B
Solution :
\[|z-1|=|z-2|=|z-i|\] (i) \[|z-1|=|z-i|\] represents a straight line through origin i.e., \[y=x\] (ii) \[|z-1|=|z-2|\Rightarrow x=\frac{3}{2}\] which is a straight line (iii) \[|z-2|=|z-i|\Rightarrow 4x-2y=3\] which is a straight line \[|z-1|=|z-2|=|z-i|\] can represent a triangle.
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