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Consider the surfaces x^2+2y^2-z^2+3x=1 and 2x^2+4y^2-2z^2-5y=0.

a. What is the name of each surface?

b. Find an equation for the plane which contains the intersection of these two surfaces.

That is the question. For "a", I generally know what needs to be done, but I can't figure out how to get the equations into the form of a standard quadric surface equation. Do I just complete the square, or what? Also, I really have no idea how to do "b". Can someone solve this and please explain to me how to do it? Thanks in advance.