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
- FREE FTCE Math Practice Test
- How to Evaluate Integers Raised to Rational Exponents
- A Comprehensive Collection of Free CLEP College Mathematics Practice Tests
- How long Is the SHSAT Test?
- Mastering the Art of Teaching Pre-Algebra with “Pre-Algebra for Beginners”
- 7th Grade FSA Math Practice Test Questions
- How to Multiply Polynomials Using Area Models
- 7th Grade NYSE Math Worksheets: FREE & Printable
- Best Online Math Tutoring Equipment
- The Butterfly Effect in Mathematics: Small Changes, Big Impact
What people say about "Standard Form of a Circle - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.