Let p be a non-zero constant. A point P(x,y) moves so that its distance from the point (p,0) is equal to its perpendicular distance from the line x=−p.
(i) Derive the Cartesian equation satisfied by P.
(ii) For p=−23, write the specific equation obtained in part (i).
(iii) For the equation found in part (ii), state the coordinates of the focus, the equation of the directrix and the length of the latus rectum.
(iv) Calculate the coordinates of the points where the parabola in part (ii) intersects the y-axis.