How to Find the Center and the Radius of Circles? (+FREE Worksheet!)
To find the center and radius of a circle from its equation, you need to find the equation of the circle in is the center-radius form.
Related Topics
- How to Find Arc Length and Sector Area
- How to Find Equation of a Circle
- How to Find the Area and Circumference of Circles
Rules for Finding the Center and the Radius of Circles
To find the center and the radius of a circle using the equation of the circle:
- Write the equation of the circle in standard form: \((x- h)^2+( y-k)^2= r^2\),
- The center of the circle is at \(h,k\), and its radius is \(r\).
Find the Center and the Radius of Circles – Example 1:
Identify the center and the radius of each circle.
\(x^2+ y^2-4x+3=0\)
Solution:
\((x- h)^2+( y-k)^2= r^2\) is the circle equation with a radius \(r\), centered at \(h,k\).
Rewrite \(x^2+ y^2-4x+3=0\) in the standard form:
\(x^2+ y^2-4x+3=0→(x-2)^2+(y-0)^2=1^2 \)
Then, the center is at: \((2,0)\) and \(r=1\)
The Absolute Best Book for the Algebra I
Find the Center and the Radius of Circles – Example 2:
Identify the center and the radius of each circle.
\(8x+x^2+10y=8- y^2\)
Solution:
\((x- h)^2+( y-k)^2= r^2\) is the circle equation with a radius \(r\), centered at \(h,k\).
Rewrite the equation in standard form:
\(8x+x^2+10y=8- y^2→(x-(-4))^2+(y-(-5))^2=7^2 \)
Then, the center is at \((-4,-5)\) and the \(r=7\).
Find the Center and the Radius of Circles – Example 3:
Identify the center and radius.
\(8x+x^2-2y=8- y^2 \)
Solution:
\((x- h)^2+( y-k)^2= r^2\) is the circle equation with a radius \(r\), centered at \(h,k\).
Rewrite \(8x+x^2-2y=8- y^2\) in the standard form:
\((x-(-4))^2+(y-1)^2=5^2\)
Then, the center is at \((-4,1)\) and \(r=5\)
The Absolute Best Book for the Algebra Test
Related to This Article
More math articles
- SSAT Upper-Level Math Worksheets: FREE & Printable
- 4th Grade Wisconsin Forward Math Worksheets: FREE & Printable
- How to Find Domain and Range of Relations
- Top 10 Tips to Overcome ASTB Math Anxiety
- 6th Grade Georgia Milestones Assessment System Math FREE Sample Practice Questions
- How to Remove Ambiguity in Infinite Limits
- HL Congruence: The Special Case of Right Triangles
- How to Find the Period of a Function?
- The Ultimate SSAT Upper Level Math Formula Cheat Sheet
- What Are the Applications of Inverse Trigonometric Functions?
What people say about "How to Find the Center and the Radius of Circles? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.