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.
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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=r2,
- 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.
x2+y2−4x+3=0
Solution:
(x−h)2+(y−k)2=r2 is the circle equation with a radius r, centered at h,k.
Rewrite x2+y2−4x+3=0 in the standard form:
x2+y2−4x+3=0→(x−2)2+(y−0)2=12
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+x2+10y=8−y2
Solution:
(x−h)2+(y−k)2=r2 is the circle equation with a radius r, centered at h,k.
Rewrite the equation in standard form:
8x+x2+10y=8−y2→(x−(−4))2+(y−(−5))2=72
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+x2−2y=8−y2
Solution:
(x−h)2+(y−k)2=r2 is the circle equation with a radius r, centered at h,k.
Rewrite 8x+x2−2y=8−y2 in the standard form:
(x−(−4))2+(y−1)2=52
Then, the center is at (−4,1) and r=5
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