Which of the following is the correct equation for a circle centered at (h, k)?

The equation for a circle centered at the point (h, k) is correctly represented as (x - h)² + (y - k)² = radius². This form clearly indicates how each point (x, y) on the circle relates to its center.

In this equation, (x - h)² measures the horizontal distance from the center of the circle to any point on the circle, and (y - k)² measures the vertical distance from the center to that same point. The radius squared on the right side of the equation provides a constant value that sets the maximum distance from the center to the points that make up the circle.

This format is essential for describing circles in the Cartesian coordinate system, as it centers the circle around the specified coordinates (h, k) and encapsulates all the points at a distance equal to the radius from this center.