Find parametric equations for the cylinder $y ^ { 2 } + z ^ { 2 } = 49$
A) $\vec { r } ( s , \theta ) = 7 \cos \overrightarrow { \theta i } + 7 \sin \theta \vec { j }$
B) $\vec { r } ( s , \theta ) = 7 \cos \theta \vec { i } + 7 \sin \theta \vec { j } + s \vec { k }$
C) $\vec { r } ( s , \theta ) = s \vec { i } + 49 \cos \theta \vec { j } + 49 \sin \theta \vec { k }$
D) $\vec { r } ( s , \theta ) = \operatorname { si } + 7 \cos \theta \vec { j } + 7 \sin \theta \vec { k }$
E) $\vec { r } ( s , \theta ) = \operatorname { si } + 7 \cos \theta \vec { j } + 7 \cos \theta \vec { k }$

Question

Quizplus · Accepted Answer

The given equation $y^2 + z^2 = 49$ describes a cylinder with radius 7 centered along the x-axis. The correct parametric equations must allow $y$ and $z$ to vary with the circle of radius 7, while $x$ can be any real number (represented by $s$ in this context). Choice D correctly represents this with $x = s$, $y = 7\cos\theta$, and $z = 7\sin\theta$, covering all points on the cylinder.

Find Parametric Equations for the Cylinder y2+z2=49y ^ { 2 } + z ^ { 2 } = 49y2+z2=49

Find Parametric Equations for the Cylinder $y ^ { 2 } + z ^ { 2 } = 49$