What you’ll learn
Identify center/radius from equation.
Key idea
The positive square root of the right-side constant is the radius, not the constant itself.
Zero the offsets for center and take a positive square root for radius.
Worked example
Classify examples and non-examples for the concept 'Identify center/radius from equation'.
Classify circle (x+3)^2+(y-1)^2=25: select its center and radius with squared-distance evidence.
Labeled coordinates: O=(-3, 1); R=(2, 1); L=(-8, 1); U=(-3, 6); D=(-3, -4).
- The offset zeroes give center (-3,1).
- The right side is 25, whose positive square root is radius 5.
Answer: Center (-3,1), radius 5 — both offsets vanish there and sqrt(25)=5.
Quick Check
Classify examples and non-examples for the concept 'Identify center/radius from equation'.
Classify circle (x+2)^2+(y-2)^2=4: select its center and radius with squared-distance evidence.
Labeled coordinates: O=(-2, 2); R=(0, 2); L=(-4, 2); U=(-2, 4); D=(-2, 0).