My book says that Geostationary Satellites can only be found in the equatorial plane. I wonder if there would be any other planes about which they could revolve around the earth.
Lets consider what "Geostationary" actually means:
A geostationary orbit is a particular type of geosynchronous orbit, the distinction being that while an object in geosynchronous orbit returns to the same point in the sky at the same time each day, an object in geostationary orbit never leaves that position.
So we need to be above the same point on Earth all of the time.
The Earth is rotating, a point on the surface moving around west to east (ie in the equatorial direction). If your satellite moves in any direction other than this then it will diverge from the path of the point on earth that it wants to stay above.
(In case you weren't aware an orbit needs to have the center of mass of the two objects within it's orbital plane, so having an orbital plane parallel to the equatorial one but higher up wouldn't work).
Strictly speaking, the only geostationary orbits are circular equatorial orbits at a very specific altitude above the surface of the Earth.
Satellites orbit on a plane that contains the center of the Earth. A satellite in a non-equatorial circular orbit spends half of each orbit north of the equator and the other half, south of the equator. Such satellites are not geostationary. A satellite at the wrong altitude orbits at a different rate than the Earth's rotation rate. Such satellites are not geostationary. A satellite in a non-circular orbit with the right semi-major axis results in the satellite sometimes moving faster than the Earth's rotation, other times slower. Such satellites might be geosynchronous, but they are not geostationary.
In practice, all geostationary satellites exhibit these behaviors to some extent. There are always errors in the orbit placement, and there are perturbations that inevitably nudge a satellite a bit off of its intended orbit. One of the jobs of the operations center for that satellite is to track its drift from the desired geostationary orbit and occasionally correct for deviations.
Some satellites are geosynchronous (or close to it) but are far from geostationary. A special class of geosynchronous orbits are the highly inclined (by about 63.4 degrees) and highly eccentric tundra orbits. The large eccentricity means the satellite spends a good portion of each orbit in a nearly stationary position near apogee. These address a key issue with geostationary satellites, which is that geostationary satellites aren't particularly useful as communications satellites north of about 60 degrees north latitude due to the low elevation angle at those high latitudes. The tundra satellites have their apogees near the northernmost reach of their orbits, making them nearly geostationary for about 1/3 of their orbits.
A related concept are the Molniya orbits. These too are highly eccentric orbits, but their period is half a day. The nearly hover over two northern spots twice daily. The Soviet Union (and now Russia) made extensive use of these orbits. The satellites spend a good portion of each orbit either high over northern North America (good for spying) or high over Russia (good for communications).
Let's imagine that a satellite is geostationary over a point at 42 latitude (e.g. not over the equator). In this case, the satellite must always be found at 42 Latitude.
Because the Earth is (approximately) a sphere, we may approximate the earth as a point particle. If we do this, the satellite is not orbiting the centre of the Earth, but instead orbiting a point away from the centre of the Earth (which would be unphysical).
Any other orbit will not be geostationary, since the Earth will move (rotate) under the satellite as it orbits.
Previous answer is correct. However, IIRC, if your launch site is at high latitude so cannot practicably access equatorial orbit, you may mimic the coverage using several satellites sharing a very elliptical orbit. This lets each spend a significant proportion of each orbit in same narrow band of sky, so a fixed antenna should still work.
Downside, such orbit may be much more sensitive to geoid variation, MasCons etc when 'low', then Lunar position when 'high' so need more frequent tweaks than a genuine GeoSat's, so burn through more station-keeping fuel...
This answer only works if you take the definition of geostationary orbit as an orbit that allows for the satellite to be constantly directly above a point on the planet.
Imagine you place some perpendicular poles down on some points on earth. One on the equator and one at anywhere else (let's say Australia ). Now you trace out the path traveled by the tip of the pole as the earth rotates. You should get two circles.
The circle by the pole of the equator should be centered at the center of earth, which is allowed as the force of gravity is canceled out by the centrifugal force of the satellite as it orbits (might not be accurate but should get the point across ). The path in which the satellite travels is in line with the force of gravity that acts on it. (The path is the circle traced out, while imagine the force of gravity as the radius of the circle.)
On the other hand, the pole at Australia would trace out a circle which is centered below the centre of the earth. In this case the direction of the force of gravity will not be aligned with the centrifugal force caused by the satellite's motion. This means that if some object were to travel in this orbit it would either have to have some other forces supplied, like rocket boosters, or it will fall to an orbit where all forces are canceled out.
Just tell me if my explanation is flawed or if I need to add pictures to clarify my idea.
height of pole is not specified here because it involves knowing the geostationary orbit altitude.(which you need the mass of the planet and speed in which the planet rotates to find out). For this case just assume that it is a very long pole that stretches into space.