How to Write and Graph the Standard Equation of a Circle

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The following Standard Equation of a Circle Formula examples will show you everything you need to know!

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Welcome to this free lesson guide that accompanies this Standard Equation of a Circle Explained! Tutorial where you will learn the answers to the following key questions and information:

This Complete Guide to the Standard Equation of a Circle includes several examples, a step-by-step tutorial, an animated video mini-lesson, and a free equation of a circle worksheet and answer key.

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Standard Equation of a Circle Definition

Before you learn the standard equation of a circle formula, let’s quickly review the basic properties of circles:

Notice that the terms are in reverse order!

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The radius of a circle is any line that extends from the center of the circle to the edge.

The diameter of a circle is any straight line that extends from one edge of the circle through the center and to the opposite side. The value of the diameter is two times the radius.

The Standard Equation of a Circle Formula:

Figure 1

The standard equation formula of a circle formula above is not as intimidating as it looks.

Let’s break it down:

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You only need to know two pieces of information to write the standard equation of a circle:

That’s it! Now let’s look at an example:

How to Find the Standard Equation of a Circle Formula

Example 1

Write the standard form equation for circle S with a center at (4,3).