Complex Numbers And Quadratic Equations question 380
Question: . Which of the following equations can represent a triangle [Orissa JEE 2005]
Options:
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 $
Show Answer
Answer:
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.
BETA
