The general form of the equation of a circle centered at the origin (0, 0) is given by:
x2 + y2 = r2
Here, r represents the radius of the circle. This equation indicates that for any point (x, y) lying on the circle, the sum of the squares of its x-coordinate and y-coordinate is equal to the square of the radius.
To understand why this is the case, consider the definition of a circle: it is the set of all points that are a fixed distance (the radius) from a central point (the center). In this scenario, since the center is located at (0, 0), the distance from any point on the circle to the center can be calculated using the Pythagorean theorem, which yields the relationship given by the equation.