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).
a. (i) Show that the length of the latus rectum is 4 units.
b. (ii) Determine the value of the parameter a associated with this parabola.
c. (iii) Write the standard Cartesian equation of the parabola.
d. (iv) Find the coordinates of the vertex and focus, and write the equation of the directrix.