Answer
Geosynchronous communication satellites have a period of 24 hours, just like the rotation of the Earth, and thus they appear to hover above a fixed point, P, on Earth. The satellite thus follows a circular path whose center is the Earth's center.
For this satellite to remain exactly overhead at point P, the point must also follow a circular path whose center is the Earth's center. This is true only if point P is on the equator.
