Surface of Revolution: Find Equation & Identify Surface

[Fernando Revilla]

I quote a question from Yahoo! Answers

Find the equation of the surface of revolution when y^2+z^2+2y=0 is revolved about y-axis. Identify the surface of revolution.

I have given a link to the topic there so the OP can see my response.

 

[Fernando Revilla]

We can express $y^2+z^2+2y=0 $ as $(y+1)^2+z^2=1$, so $\gamma\equiv y^2+z^2+2y=0,x=0$ is a circle with center $(0,-1,0)$, radius $1$, and revolving about one of its diameters. As a consquence, the corresponding surface is the sphere $E\equiv x^2+(y+1)^2+z^2=1$.