Mathematical Equation of a Circle

The standard equation of a circle with center (h, k) and radius (r) is:

(x - h)² + (y - k)² = r²

In this equation:

(h, k): Coordinates of the center of the circle.

(r): Radius of the circle, the constant distance from any point on the circle to the center.

For example, a circle centered at the origin (0, 0) with radius 3 would have the equation:

x² + y² = 9

This equation is derived using the distance formula. The distance between any point (x, y) on the circle and the center (h, k) is equal to the radius (r), which leads directly to the equation above.