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Circle Equation — result sheet
Build the standard circle equation from a center and positive radius, then return the expanded quadratic coefficients.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: (x-h)^2+(y-k)^2=r^2, or x^2+y^2+D*x+E*y+F=0 with D=-2h, E=-2k, F=h^2+k^2-r^2.
The center shifts the two coordinate axes and the positive radius sets the squared distance from the center. Expansion supplies the coefficients of x and y and the constant term in the implicit quadratic equation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Center h — coordinate units; The x-coordinate of the circle center.; minimum -1000000; maximum 1000000
- Center k — coordinate units; The y-coordinate of the circle center.; minimum -1000000; maximum 1000000
- Radius r — length units; A strictly positive circle radius.; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Center h | 2 |
| Center k | -3 |
| Radius r | 5 |
(x-2)^2+(y+3)^2=25; expanded form is x^2+y^2-4x+6y-12=0, so D=-4, E=6, and F=-12.
Assumptions and limits
- The circle lies in a flat two-dimensional Cartesian plane with one shared coordinate unit.
- The center coordinates are finite and the radius is strictly positive; no degenerate point-circle is accepted.
- The returned coefficients describe the equation only and do not calculate area, circumference, intersections, or a fitted circle.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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