Circle $$C_{1}$$ has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel to the X axis. P and Q are points on curves given by the equations $$y = a^{x} and y = 2a^{x}$$ respectively, where a < 1. The value of a is:

A

$$\frac{1}{\sqrt[6]{2}}$$

B

$$\frac{1}{\sqrt[6]{3}}$$

C

$$\frac{1}{\sqrt[3]{6}}$$

D

$$\frac{1}{\sqrt{6}}$$

E

None of the above