Standard Form of a Circle
The equation of a circle is written using the radius and center of the circle.

The equation of the circle is shown with the center and radius of the circle. With this information, we can sketch the graph of the circle.
Related Topics
Step by Step Guide to Write the Standard Form of a Circle
- The Standard form of a circle is \((x- h)^2+( y-k)^2= r^2\), where \(r\) is the radius and \((h, k)\) is the center. By knowing the center and radius of the circle we can write the standard form of a circle.
Standard form of a Circle – Example 1:
Write the standard form equation of circle with center: \((0, 5)\), radius: \(3\)
Solution:
The Standard form of a circle is \((x- h)^2+( y-k)^2= r^2\), where \(r\) is the radius and \((h, k)\) is the center.
In this case, the center is \((0, 5)\) and the radius is \(3\): \((h, k)=(0, 5), r=3\)
Then: \((x- 0)^2+( y-5)^2= 3^2 → x^2+( y-5)^2= 9 \)
Standard form of a Circle – Example 2:
Write the standard form equation of the circle \(x^2+y^2-6x+2y= 6\).
Solution:
The Standard form of a circle is \((x- h)^2+( y-k)^2= r^2\), where \(r\) is the radius and \((h, k)\) is the center.
Group \(x\)-variables and \(y\)-variables together: \((x^2-6x)+( y^2+2y)= 6\)
Convert \(x\) to square form: \((x^2-6x+9)+( y^2+2y)= 6+9 → (x-3)^2+( y^2+2y)=6+9\)
Convert \(y\) to square form: \((x-3)^2+( y^2+2y+1)= 6+9+1 → (x-3)^2+(y+1)^2=6+9+1\)
Then: \((x-3)^2+(y+1)^2=4^2\)
Exercises for Writing Standard form of a Circle
Write the standard form equation of each circle with the given information.
- \(\color{blue}{Center: (0, 4)}, \color{blue}{Radius: 2}\)
- \(\color{blue}{Center: (-1, 2)}\), \(\color{blue}{Radius: 5}\)
- \(\color{blue}{x^2+y^2-6x+8y=0}\)
- \(\color{blue}{x^2+y^2-2x+8y=0}\)

- \(\color{blue}{x^2+(y-4)^2=2^2}\)
- \(\color{blue}{(x+1)^2+(y-2)^2=5^2}\)
- \(\color{blue}{(x-5)^2+y^2=4^2}\)
- \(\color{blue}{(x-1)^2+(y+4)^2=5^2}\)
Related to This Article
More math articles
- Top Calculator for the PSAT 10 Math Test: Quick Review
- Polygon Names
- How to Find the Perimeter of Polygons? (+FREE Worksheet!)
- 5th Grade PARCC Math Worksheets: FREE & Printable
- Ace the Math Subtests of the ASVAB Test
- 6th Grade RICAS Math Worksheets: FREE & Printable
- Top 10 Free Websites for ASVAB Math Preparation
- How to Multiply and Divide Decimals? (+FREE Worksheet!)
- The Ultimate PERT Math Course (+FREE Worksheets & Tests)
- 10 Most Common AFOQT Math Questions
What people say about "Standard Form of a Circle"?
No one replied yet.