What is the equation of a circle in standard form?

The equation of a circle in standard form is represented by the formula ( (x - h)² + (y - k)² = r² ). In this equation, ( (h, k) ) represents the center of the circle, and ( r ) represents the radius. This format allows us to easily identify both the center and the radius of the circle by substituting specific values for ( h ), ( k ), and ( r ).

The expression ( (x - h)² + (y - k)² = r² ) derives from the definition of a circle: the set of all points that are a fixed distance ( r ) from the center point ( (h, k) ). Therefore, any point ( (x, y) ) will satisfy this equation if it lies on the circle.

In contrast, the other options represent different types of equations. The linear equation presented in another option is used to describe straight lines, while the polynomial form given in yet another option potentially describes conic sections but is not specific to circles. The last option is structurally similar to the correct answer but involves a change of signs that represents a circle centered at ( (-h, -k)