What does the formula (x-h)²+(y-k)²=r² represent in geometry?

The formula (x-h)²+(y-k)²=r² represents the equation of a circle in a Cartesian coordinate system. In this formula, (h, k) denotes the center of the circle, while 'r' stands for the radius. Specifically, the equation states that the distance from any point (x, y) on the circle to the center (h, k) is constant and equal to the radius 'r'.

This standard form is derived from the definition of a circle as the set of all points that are a fixed distance (the radius) from a particular point (the center). Understanding this relationship is essential in geometry, as it lays the groundwork for more advanced topics involving circular shapes and properties of distances in the coordinate plane.