Question

True or False?

The graph of `x^2+y^2=1` in 3-space is a circle of radius 1 centered at the origin.

Answer

False.

`x^2+y^2=1` is a circle of radius centered at the origin in xy-plane.

But 3-space contains `z` and for each value of `z`, there is one such circle.

This means, that in 3-space `x^2+y^2=1` is a cylinder.