The length of the major axis of the ellipse is 6, and the left vertex is on the circle $(x-3)^{2}+(y-2)^{2}=4$. The left directrix is the $y$-axis, then the range of the eccentricity $e$ of the ellipse is
(A) $\left[\frac{3}{8}, \frac{3}{4}\right]$
(B) $\left[\frac{1}{4}, \frac{1}{2}\right]$
(C) $\left[\frac{1}{2}, \frac{3}{4}\right]$
(D) $\left[\frac{3}{4}, 1\right)$
6. (A).

Let the coordinates of the left vertex of the ellipse be $(3+2 \cos \theta, 2-2 \sin \theta)$. According to the definition of the ellipse, we have $3-3e=e(3+2 \cos \theta)$, thus $e=\frac{3}{6+2 \cos \theta}$. Therefore, $\frac{3}{8} \leqslant e \leqslant \frac{3}{4}$.