Describe the given set of points with a single equation or with a pair of equations.
-The circle of radius 2 centered at the point (10, -2, 2) and lying in a plane perpendicular to the x-axis
A) $( y + 2 ) ^ { 2 } + ( z - 2 ) ^ { 2 } = 4$ and $x = 10$
B) $\left( \frac { y } { - 2 } \right) ^ { 2 } + \left( \frac { z } { 2 } \right) ^ { 2 } + 1 = 4$
C) $( \mathrm { y } + 2 ) ^ { 2 } + ( \mathrm { z } - 2 ) ^ { 2 } = 4$ and $\mathrm { y } + \mathrm { z } = 0$
D) $\left( \frac { y } { - 2 } \right) ^ { 2 } + \left( \frac { z } { 2 } \right) ^ { 2 } = 4$ and $x = 10$

Question

Describe the given set of points with a single equation or with a pair of equations.
-The circle of radius 2 centered at the point (10, -2, 2) and lying in a plane perpendicular to the x-axis 
A) $( y + 2 ) ^ { 2 } + ( z - 2 ) ^ { 2 } = 4$ and $x = 10$
B) $\left( \frac { y } { - 2 } \right) ^ { 2 } + \left( \frac { z } { 2 } \right) ^ { 2 } + 1 = 4$
C) $( \mathrm { y } + 2 ) ^ { 2 } + ( \mathrm { z } - 2 ) ^ { 2 } = 4$ and $\mathrm { y } + \mathrm { z } = 0$
D) $\left( \frac { y } { - 2 } \right) ^ { 2 } + \left( \frac { z } { 2 } \right) ^ { 2 } = 4$ and $x = 10$

Quizplus · Accepted Answer

The circle is defined in a plane perpendicular to the x-axis and centered at (10, -2, 2) with a radius of 2. The equation $( y + 2 ) ^ { 2 } + ( z - 2 ) ^ { 2 } = 4$ describes a circle in the yz-plane with a radius of 2 and centered at (-2, 2). The equation $x = 10$ fixes the circle's position along the x-axis, ensuring the circle lies in a plane perpendicular to the x-axis and centered at (10, -2, 2).

Describe the Given Set of Points with a Single Equation (y+2)2+(z−2)2=4( y + 2 ) ^ { 2 } + ( z - 2 ) ^ { 2 } = 4(y+2)2+(z−2)2=4

Describe the Given Set of Points with a Single Equation $( y + 2 ) ^ { 2 } + ( z - 2 ) ^ { 2 } = 4$