If `z` is complex number, then the locus of `z` satisfying the condition `|2z-1|=|z-1|` is perpendicular bisector of line segment joining 1/2 and 1 circle parabola none of the above curves

Options

A. perpeciular bisector of line segment joining 1/2 and 1
B. circle
C. parabola
D. none of the above curves

Answer

B

Explanation

`2|z-(1)/(2)|=|z-1|`
`therefore (|z-1|)/(|z-(1)/(2)|)=2`
So, locus of z is a circle.