Shifting of origin

Let us suppose we have a point P in the plane. We have a cartesian coordinate system XY such that the coordinates of this point P with reference to this frame is (x,y). Now,let us shift the coordinate axis system to a point (h,k) and let us call this new coordinate system X'Y' and the x and y coordinates of a point be represented by X and Y. So,according to the diagram below,X=(x-h), Y=(y-k). Hence,the coordinates of a point change to (x-h,y-k) whenever the coordinate axis system gets shifted to a point (h,k). This concept is useful in determining the equation of curve in a plane in the new coordinate system as shown below.