Parabola: Latus Rectum

How to find the latus rectum of a parabola: formula, 3 examples, and their solutions.

Formula: y2 = 4px

Formula

The latus rectum of a parabola is a segment
that passes through the focus
and that is parallel to the directrix.
(brown segment)

Parabola: Equation

For the parabola y2 = 4px,
the length of the latus rectum is
|4p|.

Example 1

Example

Solution

y2 = 8x

Then the latus rectum is
|8|.

So 8 is the answer.

Example 2

Example

Solution

y2 = -12x

Then the latus rectum is
|-12|.

|-12| = 12

So 12 is the answer.

Formula: x2 = 4py

Formula

For the parabola x2 = 4py,
the length of the latus rectum is
|4p|.

Example 3

Example

Solution

Switch both sides.

Divide both sides by 3.

Then x2 = [1/3]y.

x2 = [1/3]y

Then the latus rectum is
|1/3|.

|1/3| = 1/3

So 1/3 is the answer.