What you’ll learn
Write circle equation from center/radius.
Key idea
A circle equation sums squared offsets and equals radius squared.
Center offsets use subtraction and the equation right side is radius squared.
Worked example
Enter the exact value or ordered values in the format requested below.
A circular boundary has center (-3,1) and radius 5. Write its full standard equation in x,y.
Labeled coordinates: O=(-3, 1); R=(2, 1); L=(-8, 1); U=(-3, 6); D=(-3, -4).
- Offsets are x-(-3), y-(1); radius squared is 25.
- The full equation (x+3)^2+(y-1)^2=25 contains each cardinal point, including (2,1).
Answer: (x+3)^2+(y-1)^2=25
Quick Check
Choose which candidate representation satisfies the requirements of 'Write circle equation from center/radius' and justify the choice.
For center (-2,2) and radius 2, select from (x+2)^2+(y-2)^2=4, (x-2)^2+(y+2)^2=4, (x+2)^2+(y-2)^2=2; justify both constraints.
Labeled coordinates: O=(-2, 2); R=(0, 2); L=(-4, 2); U=(-2, 4); D=(-2, 0).