JEE Math Practice Question

Let $$x = 2t$$, $$y = {{{t^2}} \over 3}$$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $$SA \bot BA$$, where A is any point on the conic. If k is the ordinate of the centroid of the $$\Delta$$SAB, then $$\mathop {\lim }\limits_{t \to 1} k$$ is equal to :

1. A.$${{17} \over {18}}$$
2. B.$${{19} \over {18}}$$
3. C.$${{11} \over {18}}$$
4. D.$${{13} \over {18}}$$