A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is $\frac{1}{2}$. Then the length of the semi-major axis is

Question

( A ) $\frac{8}{3}$
( B ) $\frac{4}{3}$
( C ) $\frac{2}{3}$
( D ) $\frac{5}{3}$