A straight line l passes through the origin and has slope 2. A point A(6,0) is fixed on the x-axis.
(i) Obtain the equation of l.
(ii) A point P moves on l such that the distance OP is equal to the distance PA. Find the coordinates of P.
(iii) Verify, by direct substitution, that your answer in part (ii) satisfies the required equality of distances.