question_answer

If\[W=\frac{z}{z-\frac{1}{3}i}\]and\[|w|=1,\]then z lies on     AIEEE  Solved  Paper-2005

A) a parabola        

B)        a straight line

C)                        a circle            

D)        an ellipse

Correct Answer: B

Solution :

Ifthen z lies on a circle ofand z lies on a perpendicular bisector of segment with end pointsand .if. Given that, and z lies on perpendicular bisector of (0, 0) and So, z lies on a straight line. Alternate Solution Since, and     Let     which shows that z lies on a straight line.