Question

For each of the following equtions describe the surface and identify the traces. What does it mean by traces? x^2+y^2-2z=0

Thank you very much for your help!!!

Answer 1

means the set of all points that fit this equation
http://www.wolframalpha.com/input/?i=x^2%2By^2-2z%3D0

Answer 2

oooh "traces" my fault

Answer 3

cross section parallel to a plane
\(xy\) trace, set \(z=0\) for example

Answer 4

so in this case the \(xy\) trace is given by the equation \(x^2+y^2=0\) which is a point at the origin of the \(xy\) plane

Answer 5

and the \(xz\) trace is \(x^2-2z=0\) or \(x^2=2z\) a parabola

Answer 6

Ok, I understand. Thank you!