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 + ( y - 1)^2 + z^2 = 4, y = 0

Question
Equations
asked 2020-12-17
Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. \(\displaystyle{x}^{{2}}+{\left({y}-{1}\right)}^{{2}}+{z}^{{2}}={4},{y}={0}\)

Answers (1)

2020-12-18
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 \(\displaystyle\sqrt{{{3}}}\).
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