The length of the minor axis (along y-axis) of an ellipse

Question:

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

  1. $\sqrt{\frac{5}{6}}$

  2. $\frac{1}{2} \sqrt{\frac{11}{3}}$

  3. $\frac{1}{3} \sqrt{\frac{11}{3}}$

  4. $\frac{1}{2} \sqrt{\frac{5}{3}}$


Correct Option: , 2

Solution:

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