Circle C, 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−ax and y−2a respectively, where a<1. The value of a is:

PQ is parallel to X-axis => y-coordinates of P and Q are same and the x-coordinates differ by 6 (as the diameter is 6).
Q is a point on y = 2a => y coordinate of both P and Q is equal to 2a units.
P is a point on y = ax => x coordinate of P is 2 units => x coordinate of Q can be either -4 or 8.
We cannot say anything about the value of a from this information. So, the value of a cannot be determined.

answer is 2^(1/6)
but how????
this is how it was solved

a^p=2a^(p+6)
=> p=2^(1/6)