When a satellite has an elliptical orbit, the plane of the orbit
A. sometimes passes through the centre of earth
B. does not pass through the centre of earth
C. passes through the centre of earth always
D. none of the above.

Hint: Using Kepler's first law if the satellite has an elliptical path around the earth, then the earth is located at one of the foci of the elliptical path. As the foci of the ellipse lie in the plane of the ellipse therefore the centre of the earth must also lie in the plane of the elliptical orbit.

Complete answer:
When a satellite has an elliptical orbit the plane of the orbit passes through the centre of the earth always.
According to Kepler's first law if the satellite has an elliptical path around the Earth the earth must lie at one of the foci of the elliptical path. Since the foci of the ellipse lies in the plane of the ellipse therefore the centre of the earth lies in the plane of the elliptical path. An elliptical path is traced in such a way that the distances from a single point over the curve to the two foci always remains constant.

Hence the correct option is (B).

Note: The type of path that will be taken up by an unpowered space vehicle starting at a given location will depend upon its velocity. It will take up an open-ended path if its velocity equals or exceeds escape velocity; escape velocity is, by definition, that velocity required at a given location to establish a parabolic orbit. Velocities greater than escape velocity result in hyperbolic orbits. Lower velocities result in closed elliptical orbits-the vehicle is tied to the neighbourhood of the planet.