Find the equation for the surface of revolution by revolving

about thex- axis

Okay, this is far as i can get

What should i do to solve this?

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- Jun 6th 2012, 11:49 AMicelatedFind the equation for the surface of revolution by revolving
Find the equation for the surface of revolution by revolving

about the*x- axis*

Okay, this is far as i can get

What should i do to solve this? - Jun 6th 2012, 12:28 PMReckonerRe: Find the equation for the surface of revolution by revolving
Are you sure that the question asks for revolution about the

*y-axis*? Because that doesn't make a lot of sense to me. The equation defines a plane curve in the -plane, which would be perpendicular to the -axis. The axis of revolution should be in the same plane as the generating curve. - Jun 6th 2012, 12:32 PMicelatedRe: Find the equation for the surface of revolution by revolving
Sorry, i meant x-axis

- Jun 6th 2012, 12:47 PMReckonerRe: Find the equation for the surface of revolution by revolving
Okay, that's better.

Let's let . For a fixed point on this curve , revolving the point about the -axis produces a circle parallel to the -plane whose equation is . Replacing with the independent variable gives us an equation for the resulting*surface*of revolution:

As you can see from the equation, this surface is an ellipsoid. - Jun 6th 2012, 01:30 PMicelatedRe: Find the equation for the surface of revolution by revolving
Thank you