# Describe the given set with a single equation or with a pair of equations.The se

Describe the given set with a single equation or with a pair of equations.The set of points in space equidistant from the origin and the point (0, 2, 0)
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Asma Vang
Step 1
Let the points are given by (x,y,z)
Step 2
Given that (x,y,z) is equidistant from the origin and the point (0, 2, 0).
So we equate both distances and make an equation.
$\sqrt{{\left(x-0\right)}^{2}+{\left(y-0\right)}^{2}+{\left(z-0\right)}^{2}}=\sqrt{{\left(x-0\right)}^{2}+{\left(y-2\right)}^{2}+{\left(z-0\right)}^{2}}$
$\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}=\sqrt{{x}^{2}+{\left(y-2\right)}^{2}+{z}^{2}}$
${x}^{2}+{y}^{2}+{z}^{2}={x}^{2}+{\left(y-2\right)}^{2}+{z}^{2}$ (square both sides)
${y}^{2}={\left(y-2\right)}^{2}$
y=2-y (because y=y-2 is not possible)
2y=2
y=1