Find an equation in rectangular coordinates for the equation given in cylindrical coordinates. $r = 4 z$
A) $x ^ { 2 } + y ^ { 2 } = \frac { z } { 4 }$
B) $x ^ { 2 } + y ^ { 2 } = \frac { y } { 4 }$
C) $x ^ { 2 } + z ^ { 2 } = 4 y$
D) $x ^ { 2 } + y ^ { 2 } = 16 z ^ { 2 }$
E) $x ^ { 2 } + y ^ { 2 } = 4 z$

Question

Quizplus · Accepted Answer

In cylindrical coordinates, we have $x=r\cos(	heta)$, $y=r\sin(	heta)$, and $z=z$. Substituting $r=4z$ gives $x=4z\cos(	heta)$ and $y=4z\sin(	heta)$. So we have $x^2+y^2=(4z\cos(	heta))^2+(4z\sin(	heta))^2=16z^2(\cos^2(	heta)+\sin^2(	heta))=16z^2$. Therefore, the equation in rectangular coordinates is $x^2+y^2=16z^2$.

Find an Equation in Rectangular Coordinates for the Equation Given r=4zr = 4 zr=4z

Find an Equation in Rectangular Coordinates for the Equation Given $r = 4 z$