The question is: Find the volume enclosed by the ellipse $$9x^2+4y^2=36$$ after it has been rotated about the line $$2x+y=1$$
Basically, I don't really know where to go. I tried rotating the ellipse by an angle of $tan^-1(2)$ so I could rotate a shape around the axis. But then this gives me the equation $5x^2-4xy+8y^2=36$ and I don't know how to find the volume of revolution of an equation with both an $x$ variable and $y$ variable.
Some help would be much appreciated.