# Parabola: Latus Rectum

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

## Formulay^{2} = 4px

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|.

## Exampley^{2} = 8x

Solution

Solution (Detail)

## Exampley^{2} = -12x

Solution

Solution (Detail)

y^{2} = -12x

Then the latus rectum is

|-12|.

|-12| = 12

So 12 is the answer.

## Formulax^{2} = 4py

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

the length of the latus rectum is

|4p|.

## Exampley = 3x^{2}

Solution

Solution (Detail)

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.