Given the equation of a surface of revolution $x ^ { 2 } + z ^ { 2 } - 3 y = 0 \text {, find the equation of }$ its generating curve in the yz-plane rotating about the y-axis.
A) $x = \sqrt { 3 y }$ or $z = \sqrt { 3 y }$
B) $x ^ { 2 } + z ^ { 2 } = 9 y ^ { 2 }$
C) $x ^ { 2 } + z ^ { 2 } = \sqrt { 3 y }$
D) $x = 9 y ^ { 2 }$ or $z = 9 z ^ { 2 }$
E) $x = 3 y$ or $z = 3 y$

Question

Given the equation of a surface of revolution $x ^ { 2 } + z ^ { 2 } - 3 y = 0 \text {, find the equation of }$ its generating curve in the yz-plane rotating about the y-axis. 
A) $x = \sqrt { 3 y }$ or $z = \sqrt { 3 y }$
B) $x ^ { 2 } + z ^ { 2 } = 9 y ^ { 2 }$
C) $x ^ { 2 } + z ^ { 2 } = \sqrt { 3 y }$
D) $x = 9 y ^ { 2 }$ or $z = 9 z ^ { 2 }$
E) $x = 3 y$ or $z = 3 y$

Quizplus · Accepted Answer

The generating curve in the yz-plane rotating about the y-axis is obtained by setting $x=0$ in the equation of the surface of revolution, which gives $z^2 = 3y$. This equation represents the generating curve in the yz-plane. The option mentioning $x = \sqrt{3y}$ is incorrect in the context of generating curve in the yz-plane but is included in the correct choice due to the format of the options.

Given the Equation of a Surface of Revolution x2+z2−3y=0, find the equation of x ^ { 2 } + z ^ { 2 } - 3 y = 0 \text {, find the equation of }x2+z2−3y=0, find the equation of

Given the Equation of a Surface of Revolution $x ^ { 2 } + z ^ { 2 } - 3 y = 0 \text {, find the equation of }$