Question

Length of the latus rectum of the parabola whose focus is $(-1,1)$ and directrix is $4x+3y-24=0$, is?

Answer 1

Length of latus rectum of parabola is double of distance between focus and directrix.
$d=\frac{|-1\times 4+3\times 1-24|}{\sqrt{4^2+3^2}}$
$d=5$
and
$d=2a=5$
$\Rightarrow a=\frac{5}{2}$