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General Equation of Circle Calculator

Online general circle: complete the square of x²+y²+Dx+Ey+F=0 for center (−D/2,−E/2) and radius ½√(D²+E²−4F).

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x²+y²+Dx+Ey+F=0
Coefficients
Coefficients
Constant

📖 Tutorial | General Circle

1. Definition
When D²+E²−4F>0, x²+y²+Dx+Ey+F=0 is a circle with center (−D/2,−E/2) and radius ½√(D²+E²−4F).
2. Formula & Notation
D,E,FCoefficients
3. Properties & Laws
  • Complete the square;
  • r=½√(D²+E²−4F);
  • Condition >0 (=0 point, <0 none);
  • Equal x²,y² coefficients, no xy term.
4. Steps
  1. Enter D,E,F;
  2. Click "Center & Radius";
  3. Or click "Load Example".
5. Worked Examples
Example: gives center (2,3), r=2.
6. Common Pitfalls
Mind the condition;
Center is negative half;
Use −4F.

❓ FAQ | General Circle

Form?
x²+y²+Dx+Ey+F=0.
Center?
(−D/2,−E/2).
Radius?
½√...
Condition?
>0.
Example?
(2,3), r=2.
=0?
Point circle.