JEE Math Practice Question

The length of the minor axis (along y-axis) of an ellipse in the standard form is $${4 \over {\sqrt 3 }}$$. If this ellipse touches the line, x + 6y = 8; then its eccentricity is :

1. A.$${1 \over 3}\sqrt {{{11} \over 3}} $$
2. B.$${1 \over 2}\sqrt {{5 \over 3}} $$
3. C.$$\sqrt {{5 \over 6}} $$
4. D.$${1 \over 2}\sqrt {{{11} \over 3}} $$