Let $\left| \frac { \bar { z } - i } { 2 \bar { z } + i } \right| = \frac { 1 } { 3 } , z \in C$, be the equation of a circle with center at $C$. If the area of the triangle, whose vertices are at the points $( 0,0 ) , \mathrm { C }$ and $( \alpha , 0 )$ is 11 square units, then $\alpha ^ { 2 }$ equals:\\
(1) 50\\
(2) 100\\
(3) $\frac { 81 } { 25 }$\\
(4) $\frac { 121 } { 25 }$