What is the standard form of the equation of a circle?

The standard form of the equation of a circle is represented as ((x - h)² + (y - k)² = r²). In this formula, ( (h, k) ) represents the coordinates of the center of the circle, and ( r ) denotes the radius. The squared terms ( (x - h)² ) and ( (y - k)² ) indicate a distance from the center to any point on the circle, confirming that all points on the circle are equidistant from the center.

This formulation allows for a clear geometrical interpretation, where varying ( x ) and ( y ) values will describe the boundary of the circle as long as they satisfy the equation. Specifically, if you have the center's coordinates and the radius, you can easily graph the circle based on this equation.

The other options do not reflect the specific structure associated with a circle's equation in standard form. For instance, ( (x + h)² + (y + k)² = r² ) would suggest a center at ((-h, -k)), which could mislead about the center's position. The choice of ( x² + y² = r²