A parabola opens upward and has its latus rectum lying on the horizontal line y=4 with end-points at (3,4) and (−1,4).
(i) Show that the length of the latus rectum is 4 units.
(ii) Determine the value of the parameter a associated with this parabola.
(iii) Write the standard Cartesian equation of the parabola.
(iv) Find the coordinates of the vertex and focus, and write the equation of the directrix.