Quadric surfaces

[DWill]

1. The problem statement, all variables and given/known data
Reduce the equation to one of the standard forms, classify the surface, and sketch it:

4x = y^2 - 2z^2

2. Relevant equations

3. The attempt at a solution
I really don't know what to do for this one because most of the equations I've seen like this involved x^2.

Unrelated to this question: For doing these kinds of problems do you find the cross sections on each plane and then sketch it? For example, if the equation is x^2 + 4y^2 + z^2 = 4, you set one variable at a time to k:

x=k: 4y^2 + z^2 = 4 - k^2
y=k: x^2 + z^2 = 4 - 4k^2
z=k: x^2 + 4y^2 = 4 - k^2

So you can see the cross sections on each plane will be ellipses?

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2nd problem:

1. The problem statement, all variables and given/known data
Find an equation for the surface obtained by rotating the line x = 3y about the x-axis.

3. The attempt at a solution
I know this is a cone about the x-axis, but not sure how to get the exact equation.

[D H]

I really don't know what to do for this one because most of the equations I've seen like this involved x^2.


So change the names of the variables.

Look at it this way: The standard form for a parabola is y=ax^2+bx+c. x=ay^2+by+c is also a parabola.