How to Find the Center and the Radius of Circles? (+FREE Worksheet!)
How to Find the Center and the Radius of Circles? (+FREE Worksheet!) is a multiple-choice math challenge from Effortless Math. Read the problem, choose from the answer options below, then open the solution to see the full step-by-step working and check your reasoning against it.
- 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:
(x^2+ y^2-4x+3=0)
Find the Center and the Radius of Circles: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Match the formIdentify the conic by its equation pattern.
- Read featuresFind the center, vertex, radius, axes, foci, or asymptotes.
- Sketch from anchorsPlot key points first, then draw the curve.
Worked examples
Circle center and radius
- Compare to circle standard form.
- The center is (4, -1).
- The radius is the square root of 25.
Parabola direction
- The x part is squared.
- The parabola opens up or down.
- The positive coefficient means it opens up.
Try one before moving on
Find the Center and the Radius of Circles: pop-up practice
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)
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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)
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