   Chapter 16.6, Problem 30E

Chapter
Section
Textbook Problem

Find parametric equations for the surface obtained by rotating the curve x = 1/y, y ⩾ 1, about the y-axis and use them to graph the surface.

To determine

To find: The parametric equations for the surface obtained by rotating the curve x=1y,y1 , about the y-axis and to graph the surface.

Explanation

Given data:

The surface is obtained by rotating the curve x=1y,y1 , about the y-axis.

Formula used:

Write the expression for parametric equations when the surface is obtained by rotating the curve x=f(y),ya about the y-axis.

x=f(y)cosθ,y=y,z=f(y)sinθ,ya,0θ2π (1)

Here,

θ is the angle of rotation about the y-axis.

Calculation of Parametric equations of the surface:

As the surface is obtained by rotating the curve x=1y,y1 , about the x-axis, substitute 1y for f(y) and apply the limits of y-parameter in equation (1) as follows

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