Q67. Let the line $2 x + 3 y - \mathrm { k } = 0 , \mathrm { k } > 0$, 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 $x ^ { 2 } + y ^ { 2 } - 3 x - 2 y = 0$ and the length of the latus rectum of the ellipse $x ^ { 2 } + 9 y ^ { 2 } = k ^ { 2 }$ is $\frac { m } { n }$, where $m$ and $n$ are coprime, then $2 \mathrm {~m} + \mathrm { n }$ is equal to\\
(1) 11\\
(2) 10\\
(3) 12\\
(4) 13