A geostationary satellite does not trace a path over the surface of the earth because that is what geostationary means - the satellite is stationary over a point on the Earth.
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A geostationary orbit will keep the satellite in one area
relative to the surface
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Geostationary satellites are in an orbit that's 22,282 mi
(35,786 km) above the surface of the Earth. For more on
Geostationary satellite orbits, visit
http://www.idirect.net/Company/Satellite-Basics/How-Satellite-Works.aspx