# What Is the Basic Equation of a Circle? (Mathematics Lesson)

# What Is the Basic Equation of a Circle?

The equation of a circle centered at the origin is:where

**r**is the radius of the circle.

# Real Examples of Equations of Circles

- 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:

# Why the Equation of a Circle Works

The slider below explains the equation of a circle:# The Equation of a Circle that Is Not Centered at the Origin

The equation of a circle discussed above is for circles centered at the origin.If a circle is not centered at the origin, but at a point

**(a, b)**, the equation of a circle is:

Read more about the equation of a circle that is not centered at the origin

##### Curriculum

##### Interactive Test

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##### Note

**WHAT IS A CIRCLE?**

A circle is a shape containing a set of points that are all the same distance from a given point, its center.

**WHAT DOES AN EQUATION OF A CIRCLE MEAN?**

A circle is a set of points.

Each point can be described using Cartesian coordinates:

**(x, y)**.

For each point there is a relationship between

**x**and

**y**, given by the equation:

This is true for

**all**points on the circle.

For example, a circle has a radius of 2. Its equation is:

**x**

^{2}+ y^{2}= 4Consider the point at

**(2, 0)**.

At this point

**x = 2**and

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

**2**

^{2}+ 0^{2}= 4The equation is satisfied.

Consider another point

**(√2, √2)**:

At this point

**x = √2**and

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

**√2**

^{2}+ √2^{2}= 2 + 2 = 4Again, the equation is satisfied.