Let $A\left(\frac{3}{\sqrt{a}}, \sqrt{a}\right) a>0$ be a fixed point in the $x y$-plane. The image of $A$ in $y$-axis be $B$ and the image of $B$ in $x$ axis be C . If $\mathrm{D}(3 \cos \theta$, a $\sin \theta)$ is a point in the fourth quadrant such that the maximum area of $\triangle \mathrm{ACD}$ is 12 square units, then a is equal to $\_\_\_\_$。