If vertex of parabola is $\left(2,-1\right)$ and equation of its directrix is $4x-3y=21$, then the length of latus rectum is

Plotting the graph with given data we have,

We know that, in any parabola, the length of the latus rectum $=4a$ and perpendicular distance from vertex to the directrix $=a$

So, $a=\left|\frac{8+3-21}{\sqrt{4^2+{\left(-3\right)}^2}}\right|$

$\Rightarrow a=\left|\frac{-10}{5}\right|=2$ 

Therefore, the length of the latus rectum $4a=4\times 2=8$