$\text{ If the length of the latus rectum of the parabola }169\left\{(x-1{)}^2+(y-3{)}^2\right\}=(5x-12y+17{)}^2\text{ is }L\text{ then the value of }13L\text{ is }$

$\text{ Here, }(x-1{)}^2+(y-3{)}^2={\left\{\frac{5x-12y+17}{\sqrt{5^2+(-12{)}^2}}\right\}}^2$

$\therefore \text{ the focus }=(1,3)\text{ and the directrix is }5x-12y+17=0$

The distance of the focus from the directrix

$\begin{array}{r}=\left|\frac{5\times 1-12\times 3+17}{\sqrt{5^2+(-12{)}^2}}\right|=\frac{14}{13}\\ \therefore \text{ latus rectum }=2\times \frac{14}{13}=\frac{28}{13}\end{array}$