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Surface of revolution

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661
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

Well-known member
MHB Math Helper
Jan 29, 2012
661
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 $E\equiv x^2+(y+1)^2+z^2=1$.