What is the shape traced by the tip of shadow by a tilted stick?

Question

Information needed to solve this question

Assume that the sun moves in a circle around the celestial pole on the celestial sphere. The sun (depending on the specific situation) may or may not go under the horizon.

In general the celestial pole is at a altitude equal to latitude of the place.

Assume that the stick is tiled in any arbitrary fashion.

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The Question

What will be the shape of the curve traced by the tip of shadow of stick? Try to give a one line answer instead of mathematically bashing it out using spherical trigonometry.

Answer 1

The path of the sun is a circle. The projection of this circle on the ground with the tip of the stick being the reflection point will always be a conic.

Hint - the projection is a cone which is cut by the ground (a plane) giving rise to a conic.

The conic will be a ellipse or a hyperbola depending on whether the sun remain over the horizon for the whole day or not.