A curve is defined as the locus of a point that is equidistant from the point F(0,−4) and the line y=4.
(a) Derive the equation of the curve in Cartesian form.
(b) Determine the coordinates of its focus, the equation of its directrix and the length of its latus rectum.
(c) Find the coordinates of the points at which the curve meets the x-axis.