Mathematics - Ellipse Question with Solution | TestHub

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