The light source is usually placed at the focus, so the focus-vertex distance is p=3 ft. The equation for the parabola with its vertex at the origin is ...
y = 1/(4p)x^2
y = 1/12x^2
The opening for some y-value extends ±x from the axis of symmetry, so is a total of 2x in width.
Every time a new piece of equipment is added to the system, if ifs not properly optimized within the scope of the entire system, you'll end up with wasted energy and operational inefficiencies