Step 1

The given equations are \(\displaystyle{x}^{{2}}+{\left({y}−{1}\right)}^{{2}}+{z}^{{2}}={4}\) and y=0.

Substitute y=0 in \(\displaystyle{x}^{{2}}+{\left({y}−{1}\right)}^{{2}}+{z}^{{2}}={4}\) and simplify as follows.

\(\displaystyle{x}^{{2}}+{\left({0}−{1}\right)}^{{2}}+{z}^{{2}}={4}\)

\(\displaystyle{x}^{{2}}+{1}+{z}^{{2}}={4}\)

\(\displaystyle{x}^{{2}}+{z}^{{2}}={4}−{1}\)

\(\displaystyle{x}^{{2}}+{z}^{{2}}={\left(\sqrt{{{3}}}\right)}^{{2}}\)

Step 2

Geometrical description:

The set of points in space whose coordinates satisfy the given pairs of equations. \(\displaystyle{x}^{{2}}+{\left({y}-{1}\right)}^{{2}}+{z}^{{2}}={4},{y}={0}\) is the circle with center origin in xz-plane and its radius is \(\displaystyle\sqrt{{{3}}}\).

The given equations are \(\displaystyle{x}^{{2}}+{\left({y}−{1}\right)}^{{2}}+{z}^{{2}}={4}\) and y=0.

Substitute y=0 in \(\displaystyle{x}^{{2}}+{\left({y}−{1}\right)}^{{2}}+{z}^{{2}}={4}\) and simplify as follows.

\(\displaystyle{x}^{{2}}+{\left({0}−{1}\right)}^{{2}}+{z}^{{2}}={4}\)

\(\displaystyle{x}^{{2}}+{1}+{z}^{{2}}={4}\)

\(\displaystyle{x}^{{2}}+{z}^{{2}}={4}−{1}\)

\(\displaystyle{x}^{{2}}+{z}^{{2}}={\left(\sqrt{{{3}}}\right)}^{{2}}\)

Step 2

Geometrical description:

The set of points in space whose coordinates satisfy the given pairs of equations. \(\displaystyle{x}^{{2}}+{\left({y}-{1}\right)}^{{2}}+{z}^{{2}}={4},{y}={0}\) is the circle with center origin in xz-plane and its radius is \(\displaystyle\sqrt{{{3}}}\).