If $\operatorname { Re } \left( \frac { z - 1 } { 2 z + i } \right) = 1$, where $z = x + i y$, then the point $(x, y)$ lies on a\\
(1) circle whose centre is at $\left( - \frac { 1 } { 2 } , - \frac { 3 } { 2 } \right)$\\
(2) straight line whose slope is $- \frac { 2 } { 3 }$\\
(3) straight line whose slope is $\frac { 3 } { 2 }$\\
(4) circle whose diameter is $\frac { \sqrt { 5 } } { 2 }$