The locus of a complex variable z satisfying z 1 z 1 2 is ........

Given ,   

|(z-1)/(z+1)| = 2 

⇒    | (x+ i y -1)/(x+ i y +1)|=2 

⇒    |(x-1) +i y|2 / |(x+1) + i y|2 = 4 

⇒    (x -1)2 + y2 = 4(x+1)2 + 4y2 

⇒     3x2 + 3y2 + 10x +3 = 0 

⇒     3(x2 +y2) + 10x+3 = 0 ,  

which is a circle .