Which of the following is true about geodesics on an ellipsoid?

• A. Any meridian is a geodesic
• B. Any parallel is a geodesic
• C. All geodesics lie on a single plane
• D. Geodesics do not exist

Answer: (A)

On a spheroid, the surface is a surface of revolution, so planes that pass through the axis cut the surface in curves that are geodesics. Those curves are the meridians: each meridian lies in a plane containing the symmetry axis, and the shortest-path direction on the surface follows that plane without turning around the axis. That symmetry makes every meridian a geodesic on the ellipsoid.

Parallels wrap around at fixed distance from the axis and generally do not minimize distance on the surface; they have nonzero geodesic curvature, so they aren’t geodesics in general (only special cases, if any, for particular shapes). Geodesics also don’t all lie in a single plane—the paths twist across latitude and longitude. And geodesics certainly exist as curves on the surface.