Mathematics

Problem

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

\frac{m}{n}

, where

m

and

n

are coprime, then

2m + n

is equal to