Most advice about home workspaces assumes you can close a door. You may not be able to. Your parent may be in the next room or in the same room, and the desk has to be built around them, not around the view you wanted.
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Start from the chair your parent uses most
Measure that chair, the path from it to the bathroom and the kitchen, and the sightline from it to where the desk will sit. Mark the desk footprint on the floor with painter's tape and sit at it for a full morning before you buy anything. If you have to turn your whole body to see your parent, the spot is wrong.
Check the sound before you check the decor
Stand at the desk with the door closed and ask someone in the room to call your name at a normal volume. Then ask them to call from the bathroom doorway. If you cannot hear a call for help over your headset, move the desk or plan a visual signal, such as a monitor you keep on your desk or a call button your parent can reach.
Count the power, the signal and the cords
Count the outlets within reach of the desk. Test the Wi-Fi signal at the exact spot, not at the router. Use a surge strip, run cords along a wall, and keep them off the path your parent walks at night. A cord across that path is the easiest hazard to fix before anyone trips over it.
Set the desk to your body
Set the chair so your feet rest flat and your elbows sit at about a right angle at the keyboard. Put the monitor at eye level so you are not leaning forward for hours. If you work on a laptop, add a stand and an external keyboard. Small adjustments here decide whether you can get through a full day without being sore by evening.
Build the route back to the desk
Time how long it takes to get from the desk to your parent. Clear the path, keep a chair out of the way, and do not place the desk behind a door your parent may need to open or beside furniture they lean on. If the route takes more than a few seconds, move the desk or change the setup.
Run a week before you commit
Work a normal week in the space before you change anything permanent. Keep a note each time you got up, turned around or stopped a call. Those notes show you where the desk is wrong. Tell whoever sets your schedule which hours you work from this room and which hours you step away, so the setup and the job agree. You do not need to settle the whole arrangement in one meeting.
When the corner works, you will notice it first in your hands and shoulders. You will stop thinking about where you are sitting, and that is the goal.