The length of the latus rectum of an ellipse is 6 units and the distance between a focus and its nearest vertex on the major axis is $\frac{5}{3}$ units. If $e$ is the eccentricity of this ellipse, then $e$ satisfies the equation

• Correct answer
  A

  $25 x^2-40 x+16=0$
• B

  $25 x^2+40 x-16=0$
• C

  $25 x^2-40 x-16=0$
• D

  $25 x^2+40 x-32=0$

Hence, the correct answer is option: 'A'.