Give parameterizations for a circle of radius 3 in 3-space perpendicular to the y-axis centered at (4, -2, 0).
A) $x = 4 + 3 \cos t , y = - 2 , z = 3 \sin t , \quad 0 \leq t \leq 2 \pi$
B) $x = 4 + 3 \cos t , y = - 2 , z = 3 \sin t , \quad 0 \leq t \leq \pi$
C) $x = 4 + 3 \cos t , y = 3 \sin t , z = - 2 , \quad 0 \leq t \leq 2 \pi$
D) $x = 4 + 3 \cos t , \quad z = 3 \sin t , \quad 0 \leq t \leq 2 \pi$
E) $x = 3 \cos t , y = - 2 , z = 3 \sin t , \quad 0 \leq t \leq 2 \pi$

Question

Quizplus · Accepted Answer

A circle perpendicular to the y-axis means it lies in the xz-plane, with the center at (4, -2, 0) and radius 3. The correct parameterization reflects these conditions, with $y = -2$ being constant and $x$ and $z$ varying with cosine and sine functions, respectively, to maintain a radius of 3.

Give Parameterizations for a Circle of Radius 3 in 3-Space x=4+3cos⁡t,y=−2,z=3sin⁡t,0≤t≤2πx = 4 + 3 \cos t , y = - 2 , z = 3 \sin t , \quad 0 \leq t \leq 2 \pix=4+3cost,y=−2,z=3sint,0≤t≤2π

Give Parameterizations for a Circle of Radius 3 in 3-Space $x = 4 + 3 \cos t , y = - 2 , z = 3 \sin t , \quad 0 \leq t \leq 2 \pi$