The equation of a circle in a Cartesian coordinate system is given by ((x - h)^2 + (y - k)^2 = r^2), where ((h, k)) is the center of the circle and (r) is its radius. This equation represents all the points ((x, y)) that are a distance (r) from the center ((h, k)). If the circle is centered at the origin, the equation simplifies to (x^2 + y^2 = r^2).
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