Why is the cover used by photographers hyperbolic?

You mean the hood. Hyperbolic hood is also called petal hood.

The purpose is to reduce the glare interference of stray light outside the shooting area to the lens.

If the hood is flat, it will block the four corners of the picture.

The petal cover is concave inward at the position corresponding to the four corners of the picture, which can "get out of the way" the light at the four corners of the picture. On the premise of not blocking the four corners of the picture, the petals of the petal cover extend forward by a light shield, which can provide better blocking effect than the round-mouth light shield.

Please refer to the landlord for the above information, thank you.

Supplement: What are the properties of hyperbola? Sorry, I don't know exactly what you want to say.