Question

The set of points \(\left\{ {{\rm{(x,y,z)}}\mid {{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}{\rm{ = 1}}} \right\}\) in a circle.

Short answer

The given statement is false.

Step-by-step solution

A variable z is not included in an equation,

When talking about \({{\rm{R}}^{\rm{3}}}\) and when a variable z is not included in an equation, it signifies that it can take any value in addition to the valid values for the variables that are mentioned. For

\(\left\{ {{\rm{(x,y,z)}}\;\;\;{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}{\rm{ = 1}}} \right\}\)

\({{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}{\rm{ = 1}}\), a circle having a radius of 1 on the \({\rm{xy}}\)-plane when\({\rm{z = 0}}\), and also on a plane \({\rm{z = k}}\) where \({\rm{k}}\)equals any other real number. It's not like a circle because this creates a cylinder-like surface.

It creates a cylinder-like surface.

Therefore, the statement is false.