# 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

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