Ok, I'm pretty much at whit's end trying to figure this review question out. Apparently my teacher forgot to mention that our book couldn't teach us everything we need to know for our test... Anyhow, the question is as follows, and I'm utterly at a loss as to what the answer is: Find the points on the surface [ 2(x^2) + (y^2) + 4(z^2) = (1) ] at which the tangent plane is parallel to the plane [ (-3x) + (y) - (2z) = (-9) ] I've tried all sorts of guesses at what the correct method would be, but the book I'm learning from offers no examples or other such answers for this type of problem. At this point I can't offer any answers I've arrived at other than the possibilty that a particular line on the given plane might intersect the surface at 2 points, but I have no idea how to find such a line, nor am I sure that this is even the proper approach. Can someone please help me out here?