prove that length of latus rectum for a parabola is 4a

Let's assume that for the extremety of the latus rectum the coordinates are (a,l)

 This point lies on the parabola so it will satisfy,

$$y^2=4ax$$

So,

$$l^2=4a\cdot a=4a^2$$

That's why 

$$l=\pm 2a$$

So the length will be 2a+2a=4a