Find the length of the latus rectum of the parabola $y^2 = 8x$.

Compare $y^2 = 8x$ with the standard form $y^2 = 4ax$: $4a = 8 \Rightarrow a = 2$. Latus rectum length = $4a = \mathbf{8}$. **Geometric meaning.** The latus rectum is the chord through the focus, perpendicular to the axis. For $y^2 = 4ax$ the focus is $(a, 0)$; plugging $x = a$ gives $y^2 = 4a^2$ ⇒ $y = \pm 2a$ ⇒ chord length $4a$.