If the center of the circle were moved from the origin to the point (H,K) and point P at (x,y) remains on the edge of the circle which could represent the equation of the new Circle
The original circle (centered at the origin) has the equation x^2 + y^2 = r^2
After translation H units along the x-axis and K units along y-axis, the equation for the translated circle, centered at (H, K) is (x-H)^2 + (y-K)^2 = r^2