x^2 + y^2 =1, is an equation of a circle

a circle

now if we add one more variable and make the equation:
x^2 + y^2 + z^2 =1

A SPHERE!!
It becomes a sphere!!!!

I was wondering what if we add one one more variable to the equation what would the shape be. Adding of one more variable added another dimension so the circle became sphere. What would a sphere become? And what happens if we keep on adding dimensions?

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