Let $x = 2 t , y = \frac { t ^ { 2 } } { 3 }$ be a conic. Let $S$ be the focus and $B$ be the point on the axis of the conic such that $S A \perp B A$, where $A$ is any point on the conic. If $k$ is the ordinate of the centroid of the $\triangle S A B$, then $\lim _ { t \rightarrow 1 } k$ is equal to\\
(1) $\frac { 17 } { 18 }$\\
(2) $\frac { 19 } { 18 }$\\
(3) $\frac { 11 } { 18 }$\\
(4) $\frac { 13 } { 18 }$