Introduction to Circle Equations and Geometry
A circle is defined geometrically as the set of all points in a two-dimensional plane that are at a constant distance (the radius $r$) from a fixed point (the center $(h, k)$). In coordinate geometry, we represent circles algebraically using equations. Understanding how to analyze these equations is essential in analytical geometry, physics (for orbital and circular motion), and computer graphics (for rendering shapes).
Circle equations are represented in two primary formats: Standard Form and General Form. Standard Form directly reveals the geometric properties (the center coordinates and the radius). General Form is an expanded quadratic equation. Converting a circle equation from General Form to Standard Form requires a mathematical technique called completing the square, which is a common topic in algebra and pre-calculus.
This calculator converts circle equations between these two forms. By entering the center and radius, or the coefficients of the general form, the solver computes the standard equation, general equation, area, circumference, and draws a visual SVG circle on a coordinate grid.