Let the line 2 x+3 y-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…

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