The point $(3,4)$ is the focus and $2 x-3 y+5=0$ is the directrix of a parabola. Its latusrectum is
The point $(3,4)$ is the focus and $2 x-3 y+5=0$ is the directrix of a parabola. Its latusrectum is
$\frac{2}{\sqrt{13}}$
$\frac{4}{\sqrt{13}}$
$\frac{1}{\sqrt{13}}$
$\frac{3}{\sqrt{13}}$
Solution
Given that focus of parabola is $(3,4)$ and equation of directrix is $2 x-3 y+5=0$
As we know, Length of the latusrectum $=2 \times$ Length of perpendicular from focus on directrix $=\left|\frac{2 \times 3-3 \times 4+5}{\sqrt{2^2+(-3)^2}}\right|=\frac{2}{\sqrt{13}}$