How do I make fog of war around a fixed Vector3 coordinate?

I saw some fog of war tutorials on the internet and they revolved on a character/camera having a spotlight around it.

My need is to have a fog of war around the center of a plane/terrain, which is a Vector3 coordinate. More like Vector2, the y coordinate doesn't matter.

The camera moves around by keyboard and rotates by mouse, but it can't leave the plane. Because it can't go infinitely, I want to make a fog of war around it. It should behave like a real fog where you go towards it, its very thin, and the closer you go to the edge, the thicker it gets, to the maximum edge of the plane.

Because the fog of war is not a dynamic thing, I would like it to be lightweight in terms of resource consumption. It would also be nice if the camera would slow down while in the fog of war to signal the user that he/she shouldn't go inside the fog :)

Thank you.