The general form of the equation of a circle with center at the point (a, b) and radius m is given by the formula:
(x – a)² + (y – b)² = m²
In this equation:
- (x, y) represents any point on the circle.
- (a, b) is the center of the circle.
- m is the radius, which is the distance from the center to any point on the circle.
This equation tells us that for any point (x, y) that lies on the circle, the sum of the squares of the differences between the x-coordinates and the center’s x-coordinate, and between the y-coordinates and the center’s y-coordinate, equals the square of the radius. It effectively describes all the points that are exactly m units away from the center (a, b). Analyzing this equation allows us to understand the circle’s position and size on a coordinate plane.