1Cademy - Standard Form of a Circles Equation

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Circle (Geometric Definition)

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Standard Form of a Circle's Equation

The standard form of the equation of a circle with center $(h, k)$ and radius $r$ is: $(x - h)^2 + (y - k)^2 = r^2$ In this equation, $(h, k)$ identifies the location of the circle's center in the coordinate plane, and $r$ is the length of the radius. When the center is at the origin $(0, 0)$ , the equation simplifies to $x^2 + y^2 = r^2$ . Recognizing or writing a circle's equation in standard form makes it straightforward to read off the center and radius, which are needed to graph the circle. If an equation is given in expanded (general) form, the technique of completing the square can be applied to both the $x$ -terms and the $y$ -terms to rewrite it in standard form.