If $p$ represents the veriable complex number $z$ and if $|2z-1|=2|z|$ then the locus of $p$ is
$\begin{array}{1 1}(1) the\; straight\; line \;x=\frac{1}{4}&(2) the \;straight \; line \;y=\frac{1}{4}\\(3) the\; straight \; line \;z=\frac{1}{2}&(4)the\; circle\;x^{2}+y^{2}-4x-1=0\end{array}$