Let A (3/(√ a), √ a ), 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 D (3 cos θ, a…

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