alleryFind the length of the latus rectum of the parabola $y^2 = 8x$.
A$2$
B$4$
C$8$
D$16$
Answer & Solution
Correct answer: C. $8$
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 $4a$.
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