I want to run a 4" vent to my bathroom from the central ac. It is located in the attic and above the bathroom. I just replaced all the ductwork for the whole house. It's probably about less than 4' to the bathroom ceiling. Do I cut into the box and install a 4" collar and run the ductwork or use a wye? The ductwork I have is 7".

If you put in a wye, it will probably take away from whichever room the duct was going to,a duct all buy itself is best,, 4 inch is usually good for a bathroom unless its bigger than average