Question

If the vertex of the parabola is $(2,-3)$ and its directrix is $4x+3y+6=0$, then the length of its latus rectum is

Answer 1

Distance of vertex from the directrix is $=\frac{|4\left(2\right)+3(-3)+6|}{\sqrt{(4{)}^2+(3{)}^3}}=1$
Length of latus rectum will be $4\times$distance of vertex from the directrix
$=4\times 1=4$