Mathematics

Problem

Let

A\left(\frac{3}{\sqrt{a}}, \sqrt{a}\right), a > 0

, be a fixed point in the

xy

-plane. The image of

A

y

-axis be

B

and the image of

B

x

-axis be

C

. If

D(3 \cos\theta, a \sin\theta)

is a point in the fourth quadrant such that the maximum area of

\Delta ACD

is 2 square units, then

a

is equal to \_\_\_\_\_\_.