The  length of the latus rectum of the parabola $289\left\{(\mathrm{x}-3{)}^2+(\mathrm{y}-1{)}^2\right\}=(15\mathrm{x}-8\mathrm{y}+13{)}^2$  is equal to

We can write the given equation  as

$\sqrt{(\mathrm{x}-3{)}^2+(\mathrm{y}-1{)}^2}=\frac{|15\mathrm{x}-8\mathrm{y}+13|}{17}$

This represents a parabola with focus at (3, 1) and directrix as 15x-8y+ 13 =0.

L= length of latus rectum

=2[distance of focus from the directrix]

$=2\frac{\left|15\right(3)-8(1)+13|}{17}=\frac{100}{17}\simeq 5.88$