[Yo-Yo]

Is it true that there is a single line circling the earth, parallel to the equator and a certain specific distance from the earth (22,000 miles, or whatever the exact number is), and that ALL geosynchronous satellites must share that one single (circle) line?

No, there are also inclined geosynchronous orbits that also orbit the Earth once in 24 hours, and crosses the equator twice, but as viewed from the Earth, carve out a figure eight path in the sky, rather than staying stationary at a single point.

The satellites for Sirius Satellite Radio Service are in inclined geosynchronous orbit, and their vertical tracks go from Canada to Argentina.

[samtheman]

Interesting. So these are called “inclined geosynchronous”. What are the fixed-over-a-single point orbits called? Just plain “geosynchronous”, or do they have their own adverb?

[Moonman62]

They also look like highly elliptical orbits because of the speeding up and slowing down.