What is the equation of a circle in standard form?

The equation of a circle in standard form is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r is the radius. This equation demonstrates that the distance from any point (x, y) on the circumference of the circle to the center (h, k) is constant and equal to r.

In the context of this equation, the square of the radius (r²) ensures that the expression remains non-negative, which is important for defining all points that maintain a fixed distance from the center. This format allows easy identification of the circle's center and radius directly from the equation.

On the other hand, the other choices serve different mathematical representations: one represents a linear equation (y = mx + b), which describes straight lines rather than circles. Another equation (x² + y² = r²) describes a circle centered at the origin (0, 0), but lacks the flexibility to indicate a different center. The last option reflects a transformation that incorrectly depicts the geometric relationship in a standard form for circles, as it uses the addition of h and k rather than the necessary subtraction to identify coordinates effectively. Thus, understanding the format is