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Let the line 2x + 3y – k = 0, k > 0, intersect the x-axis and y-axis at the points A and B, respectively. If the equation of the circle having the line segment AB as a diameter is x 2 + y 2 – 3x – 2y = 0 and the length of the latus rectum of the ellipse x 2 + 9y 2 = k 2 is n m , where m and n are coprime, then 2m + n is equal to

1. 10
2. 11
3. 13
4. 12

Correct answer: 11

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