Please find a rotation x=Px' that removes the cross-product terms, and give its equation in the x',y',z' system, and also name the quadric. 144x^2+100y^2+81z^2-216xz-540x-720z=0
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I think the first thing I would do is eliminate the first-order terms by completing the square in x and z, and then working in translated coordinates. What does that give you?
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