Floor drain in laundry room

I tiled the floor in my laundry room today, and while doing so cut a hole in the floor for a 2" floor drain in case the washing machine drain backs up.

This is not a common occurance, but it has happened 3 times in the past 3 years, and it will ruin the new ceiling I am putting in when I finish the basement if it happens again....

My plan is to tap the line into the line that between the laundry tub, and the washing machine wall drain. Does this floor drain require a P-trap?
Or can I just 90 from under the floor to the WYE fitting I will be installing between the 2 current connections.

There is about 18" between the 2 connections in the attached photo, which is where I plan to tap in for the floor drain.
(The laundry tub is very rarely used)

(The washing machine drain is getting redone as well!)

ALL drains require a P trap. These prevent sewer gases and odors from entering the house. You will have to refill the trap with water as water in an unused trap will evaporate.

Do not forget to vent it too.

If you're connecting the floor drain to the same line that your washer is on, if your washer drain is clogged, so will be your floor drain. Unless I'm misunderstanding your plan...