Question

If the vertex of a parabola is at the origin and directrix is x + 5 = 0, then its latusrectum is __________.

Answer 1

Given for a parabola
vertex is (0, 0)
and directrix is x + 5 = 0
i.e. x = −5
⇒ parabola is of form y² = 4ax
for x = − a
i.e. a = 5
∴ Length of latus rectum is 4a = 4 × 5
= 20