Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. x^2 + ( y - 1)^2 + z^2 = 4, y = 0

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