# Parabola: Latus Rectum

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

## Formula: y^{2} = 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 y^{2} = 4px,

the length of the latus rectum is

|4p|.

## Example 1

### Example

### Solution

y^{2} = 8x

Then the latus rectum is

|8|.

|8| = 8

Absolute Value

So 8 is the answer.

## Example 2

### Example

### Solution

y^{2} = -12x

Then the latus rectum is

|-12|.

|-12| = 12

So 12 is the answer.

## Formula: x^{2} = 4py

### Formula

For the parabola x^{2} = 4py,

the length of the latus rectum is

|4p|.

## Example 3

### Example

### Solution

Switch both sides.

Divide both sides by 3.

Then x^{2} = [1/3]y.

x^{2} = [1/3]y

Then the latus rectum is

|1/3|.

|1/3| = 1/3

So 1/3 is the answer.