Let $$P_1 : y=4x^2 \text{ and } P_2 : y=x^2 + 27$$ be two parabolas. If the area of the bounded region enclosed between P_1 and P_2 is six times the area of the bounded region enclosed between the line $$y = c\alpha x, \alpha > 0 \text{ and } P_1,$$ then $$\alpha$$ is equal to:

A

6

B

8

C

15

D

12