A cat uses its tail for balance. All domestic cats hate lemons,or any citrus scent of any kind. The cheetah is the only cat that can't retract its claw As cats sharpen their claws, they leave a scent signals. Glands in the feet leave secretions, letting other cats know who has been there. Even though the tail is useful for this, it is also used for communication purposes.
Cats born without tails do manage, though.
There are other methods of balancing. After cats eat, they always immediately bathe themselves. This is because their instinct tells them to get the food scent off of them so that predators will not smell the food and come after them. In France, they used to sell rabbits skinned, but with their feet still attached. The reason being it is very difficult to tell a skinned cat from a skinned rabbit without the feet.