Give a geometric description of the set of points whose coordinates satisfy the given conditions.
-$$\mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 16 , \mathrm { x } = - 5$$
A) The line tangent to the circle $y ^ { 2 } + z ^ { 2 } = 16$ at the point $x = - 5$
B) The cylinder with the radius 4 along the $x$-axis
C) The circle $y ^ { 2 } + z ^ { 2 } = 16$ in the plane $x = - 5$
D) All points more than 4 units from the origin

Question

Quizplus · Accepted Answer

The equation $y ^ { 2 } + z ^ { 2 } = 16$ represents a circle with radius 4 centered at the origin in the $yz$-plane. The equation $x = -5$ represents a plane parallel to the $yz$-plane, passing through the point $(-5,0,0)$. Therefore, the set of points whose coordinates satisfy $\mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 16 , \mathrm { x } = - 5$ is the circle $y ^ { 2 } + z ^ { 2 } = 16$ in the plane $x = - 5$.

Give a Geometric Description of the Set of Points Whose y2+z2=16,x=−5\mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 16 , \mathrm { x } = - 5y2+z2=16,x=−5

Give a Geometric Description of the Set of Points Whose $\mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 16 , \mathrm { x } = - 5$