How to Find the Focal Diameter of a Parabola

A plane curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line is called a parabola. The focal diameter of a parabola is also known as the latus rectum. It is a line segment that passes through the focus and is parallel to the directrix. The endpoints of this line will lie on the parabola. In this article, we will learn how to find the focal diameter of a parabola.

Formula to find the Focal Diameter

Focal diameter = 4a

Where a is the distance from the vertex to the focus.

Steps to find the Focal Diameter

1. Write the standard equation of the parabola.

2. Compare the given equation with the standard equation.

3. Find the value of a.

4. Then find the value of focal diameter.

Solved Examples

Let us have a look at some examples.

Example 1.

Find the focal diameter of the parabola x = -2y2.

Solution:

Given equation is x = -2y2

Rearranging the above equation, we get y2 = -½ x

Comparing it with standard equation y2 = -4ax

We get 4ax = ½ x

a = ⅛

So focal diameter = 4a

= 4× ⅛

= ½

Example 2.

Find the focus, directrix and focal diameter of the parabola x2 = 5y.

Solution:

Given x2 = 5y

Comparing this equation with the standard equation x2 = 4ay

We get 4ay = 5y

a = ⅘

Focus (0,a) = (0, ⅘)

Equation of directrix is y = -a

y = -⅘ is the required equation.

Focal diameter = 4a = 16/5.