Rotate the coordinate axes .

The transformation will make a new graph.

Now simplify find the volume of the region around the x-axis.

(I will do this problem latter. Right now I am using one of my many computers. This one does not have a gprahing program.)

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You have,

this describes your curve.

From conics you should be familar that a rotation of transforms,

Equivalently,

Thus,

Thus,

Now the problem is that this curveis nota function (if I only had a graph) and the shell formula needs to curve to be a function. So I am going to divide this curve into two curves that are functions and add their rotational volume about the y-axis. In order to do that I will first need to bring this to the form . To do that I need to solve for .

First rewrite as,

Thus,

(TO BE CONTINUED)