If the distance of a point P(x, y) from the origin(0,0) is constant, then the point P lies on a
Circle
On a circle, every point is at the same distance from a fixed point called the center.
The point P can be any point on the circle whose distance is always the same from the origin and here origin is the center of that circle.
The point P is always at the same distance from the origin, therefore, point P lies on the circle.