In this equation,

**x**and**y**are the Cartesian coordinates of points on the (boundary of the) circle.**r**is the radius of the circle.

## Real Examples of Equations of Circles

It is easier to understand the equation of a circle with examples.- A circle with a radius of
**4**will have the equation:

- A circle with a radius of
**2**will have the equation:

- A circle with a radius of
**9**will have the equation:

## Understanding the Equation of a Circle

A circle is a set of points. Each point can be described using Cartesian coordinates**(x, y)**. The equation of a circle

**x**is true for

^{2}+ y^{2}= r^{2}**all**points on the circle. It gives the relationship between the x-coordinate and y-coordinate of each point on the circle and the radius of the circle. Consider a circle with a radius of 2. Its equation is:

x

Let us consider some points on the circle.
^{2}+ y^{2}= 4## (2, 0)

Consider the point at**(2, 0)**. It has a x-coordinate of 2 and a y-coordinate of 0.

At this point

**x = 2**and

**y = 0**. Inserting these values into the equation:

2

The equation is satisfied ✔.
^{2}+ 0^{2}= 4## (√2, √2)

Consider the point at**(√2, √2)**. It has a x-coordinate of √2 and a y-coordinate of √2.

At this point

**x = √2**and

**y = √2**. Inserting these values into the equation:

√2

Again, the equation is satisfied ✔.
Any point on the circle would satisfy the equation.
^{2}+ √2^{2}= 2 + 2 = 4## Beware

## The Circle Must Be Centered at the Origin

For this equation to work, the circle must be centered at the origin of the graph:The equation will

**not**work if the circle is

**not**centered at the origin of the graph:

how to find the equation of a circle not centered at the origin

## Getting the Equation Right

The equation of a circle must have an**x**term and a

^{2}**y**added together. These is not the equations of a circle:

^{2}Don't be fooled if the equation is simply rearranged. Below are equations of circle that can put into the familiar form with a little algebra:

## You might also like...

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