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Q.

Which of the following equations can represent a triangle:

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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

answer is B.

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Detailed 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|⇒x=32which is a straight line(iii)        |z−2|=|z−i|⇒4x−2y=3which  is a straight line
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