Online College Courses for Credit

Equations of Circles

Equations of Circles

Author: chris ludbrook

1.  Create an equation of a circle from given information.

2. Find the radius and center of a circle from a given equation.

3.  Sketch circles from a given equation.



A circle is defined as the set of all points in a plane that are equidistant from a given point, and this given point is known as the center


The image at right depicts a circle with center in the first quadrant of the coordinate plane.  The ordered pair (h,k) is the center, and (x,y) represents a point on the circle.  The segment labeled r is a radius. Recall that a radius is a segment with one endpoint at a point on the circle and the other endpoint at the center. 


See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

Begin Free Trial
No credit card required

28 Sophia partners guarantee credit transfer.

286 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 26 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.


Introduction to Circles

How to create the graph of a circle from a simple equation.

Source: Khan Academy

Graphing More Complex Circles


Unfortunately, not all equations of circles are given in standard form.  Often the first step in graphing the circle is to convert the equation to standard form to identify the find the center and radius.  To do this, we must complete the square. 


Source: Integrated Mathematics 2 Notes

Completing the Square

An example that illustrates how to "complete the square".

Source: Khan Academy