This article was reviewed by Joseph Meyer. Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.
There are 10 references cited in this article, which can be found at the bottom of the page.
This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources.
This article has been viewed 53,484 times.
A circle is a two-dimensional shape made by drawing a curve. In trigonometry and other areas of mathematics, a circle is understood to be a particular kind of line: one that forms a closed loop, with each point on the line equidistant from the fixed point in the center. Graphing a circle is simple once you follow the steps.
Steps
- Note the center of the circle. The center is the point inside the circle that is at an equal distance from all of the points on the line.[1]
- Know how to find the radius of a circle. The radius is the common and constant distance from all points on the line to the center of the circle. In other words, it is any line segment that joins the center of the circle with any point on the curved line.[2]Advertisement
- Know how to find the diameter of a circle.[3] The diameter is the length of a line segment that connects two points on a circle and passes through the center of the circle. In other words, it represents the fullest distance across the circle.[4]
- The diameter will always be twice the radius. If you know the radius, you can multiply by 2 to get the diameter; if you know the diameter; you can divide by 2 to get the radius.
- Remember that a line that connects two points on the circle (also known as a chord) but does not pass through the center will not give you the diameter; it will have a shorter distance.
- Learn how to denote a circle. Circles are defined primarily by their centers, so in mathematics, a circle’s symbol is a circle with a dot in the center. To denote a circle at a particular location on a graph, simply put the location of the center after the symbol.[5]
- A circle located at point 0 would look like this: ⊙O.
- Know the equation of a circle. The standard form for the equation of a circle is (x – a)^2 + (y – b)^2 = r^2. The symbols a and b represent the center of the circle as a point on an axis, with a as the horizontal displacement and b as the vertical displacement. The symbol r represents the radius.[6]
- As an example, take the equation x^2 + y^2 = 16.
- Find the center of your circle. Remember that the center of the circle is shown as a and b in the circle equation. If there are no brackets – as in our example – that means that a = 0 and b = 0.[7]
- In the example, note that you can write (x – 0)^2 + (y – 0)^2 = 16. You can see that a = 0 and b = 0, and the center of your circle is therefore at the origin, at point (0, 0).
- Find the radius of the circle. Recall that the r represents the radius. Be careful: if the r part of your equation does not include a square, you will have to figure out your radius.[8]
- So, in our example, you have a 16 for r, but there is no square. To get the radius, write r^2 = 16; you can then solve to see that the radius is 4. Now you can write the equation as x^2 + y^2 =4^2.
- Plot the radius points on the coordinate plane. For whatever number you have for the radius, count that number is all four directions from the center: left, right, up, and down.[9]
- In the example, you would count 4 in all directions to plot the radius points, since our radius is 4.
- Connect the dots. To graph the circle, connect the points using a round curve.[10]
Expert Q&A
Tips
Expert Interview
References
- ↑ https://www.mathopenref.com/center.html
- ↑ https://www.mathopenref.com/radius.html
- ↑ https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/area-circumference-circle/a/radius-diameter-circumference
- ↑ https://www.mathsisfun.com/geometry/circle.html
- ↑ https://www.purplemath.com/modules/circle.htm
- ↑ https://www.mathsisfun.com/algebra/circle-equations.html
- ↑ https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/hs-geo-circle-expanded-equation/a/circle-equation-review
- ↑ https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/hs-geo-circle-expanded-equation/a/circle-equation-review
- ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut29_circles.htm
About This Article
To graph a circle, start by finding the center, which is represented as "a" and "b" in the equation for the circle. Then, plot the center of the circle on that point on the graph. For example, if a = 1 and b = 2, you'd plot the center at point (1, 2). Next, find the radius of the circle by taking the square root of "r" in the equation. For example, if r = 16, the radius would be 4. Finally, plot the radius in all 4 directions from the center, and connect the points with round curves to draw the circle. For tips on how to read and interpret the equation of a circle, scroll down!
Did this article help you?
⚠️ Disclaimer:
Content from Wiki How English language website. Text is available under the Creative Commons Attribution-Share Alike License; additional terms may apply.
Wiki How does not encourage the violation of any laws, and cannot be responsible for any violations of such laws, should you link to this domain, or use, reproduce, or republish the information contained herein.
- - A few of these subjects are frequently censored by educational, governmental, corporate, parental and other filtering schemes.
- - Some articles may contain names, images, artworks or descriptions of events that some cultures restrict access to
- - Please note: Wiki How does not give you opinion about the law, or advice about medical. If you need specific advice (for example, medical, legal, financial or risk management), please seek a professional who is licensed or knowledgeable in that area.
- - Readers should not judge the importance of topics based on their coverage on Wiki How, nor think a topic is important just because it is the subject of a Wiki article.