Close Earth Projection
Animation shows an object projected along a tangent to the earth's surface with different velocities. This is obviously hypothetical but should be helpful in appreciating the relation between the path and the velocity of projection.
Notice that if the velocity of projection is less than the value required for circular orbit (say vo), the centre of the earth will be at the farther focus of the possible elliptical orbit and for velocities greater than vo, the centre of the earth will be at the closer focus.