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Standard Equation of Circle Calculator

Online standard circle: enter center and radius for (x−a)²+(y−b)²=r², with a point-position check.

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(x−a)²+(y−b)²=r²
Center
x
y
r>0
Point (opt)
x
y

📖 Tutorial | Circle

1. Definition
A circle with center (a,b), radius r is (x−a)²+(y−b)²=r²; compare point distance d to r (on/in/outside).
2. Formula & Notation
Center(a,b)
3. Properties & Laws
  • Standard equation;
  • Compare d and r;
  • General x²+y²+Dx+Ey+F=0;
  • r>0.
4. Steps
  1. Enter center, radius (and a point);
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: x²+y²=25, (3,4): d=5, on.
6. Common Pitfalls
Subtract a and b;
Right side r²;
Use distance, not raw coordinates.

❓ FAQ | Circle

Standard?
(x−a)²+(y−b)²=r².
Center?
(a,b).
Point?
d vs r.
General?
x²+y²+Dx+Ey+F=0.
Example?
On.
Diameter?
Midpoint center.