Thumbing through my well worn copy of "Rocky Mountain Geology" from a college course, I'm reminded that the tectonic plates that cover the entire earth are constantly moving, as you're probably aware. During this movement along the zones where the plates come into contact (commonly known as "faults") they sometimes get "stuck" against each other. The plates can move in opposite direction from each other (one north, one south for example) or one can dive under another (subduction) or they can even move directly apart as in the Mid-Atlantinc Ridge all of which can result in the "earthquake" when the tension between the plates suddenly lets go in a rupture of the fault.
Therefore, in relation to your question, the quake is centered only where or very near to the point of disturbance between the plates...