Write the standard equation of a circle from center and radius
Result
Circle Equation
Step-by-Step Derivation
Circle Equation Formula
(x - h)² + (y - k)² = r²
The standard circle equation describes all points that are the same distance r from the center (h,k). The squared distance from any point (x,y) to the center equals r squared.
⚠Radius must be nonnegative. A radius of 0 represents a single point rather than a full circle.
How Circle Equations Work
A circle is the set of all points at a fixed distance from a center. The formula is a direct use of the distance formula with that fixed distance set to r.
Center
The point (h,k) anchors the circle.
Radius
r controls the circle size.
Squared Form
The equation uses r squared.
Graphing
Move right by h and up by k from the origin.
💡 Example: Center (2,-1), radius 3 gives (x-2)^2+(y+1)^2=9.
Applications of Circle Equations
Circle GraphingCoordinate ProofsDesign CurvesAnalytic Geometry
Frequently Asked Questions
What is a circle equation calculator?▼
It creates the standard equation of a circle from its center and radius.
What is the circle equation formula?▼
The standard form is (x-h)^2 + (y-k)^2 = r^2.
How do I use this calculator?▼
Enter center h,k and radius r, then click Calculate.
Can radius be negative?▼
No. Radius is a distance, so it must be zero or positive.
Where is circle equation used?▼
It is used in analytic geometry, graphing circles, design, and coordinate proofs.
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