# Homework Help: Parametric equation

1. Jun 19, 2014

### nameVoid

t^2,t^4,t^6

Trying to graph this

I have the traces
x=y^2 for x>=0 in xy
Also x=z^3 for z>=0 in xz
And z=y^(3/2) for y>=0 in yz

Parametricplot3d in mathematics does nothing to get a picture for this graph and drawing is proofing difficult
In general what is the best way to plot these when it's not obvious plug in for t?

Last edited: Jun 19, 2014
2. Jun 19, 2014

### SteamKing

Staff Emeritus
It's not clear what you are trying to do.

Is your function f(x,y,z) = (t^2, t^4, t^6) perhaps? Or something else?

3. Jun 20, 2014

### nameVoid

Yes that is the function of x y z
I am trying to graph it

4. Jun 20, 2014

### haruspex

I think you mean, vectorially, r(t) = (t^2, t^4, t^6), i.e. x = t^2 etc..
But from the OP,
suggests r(t) = (t^6, t^4, t^2).
It depends what range of t you want to sketch it for.
It's kind of hard to sketch 3D curves. What exactly have you been asked to do?

5. Jun 20, 2014

### nameVoid

Sketch the curve
mathematica doesn't help

Last edited: Jun 20, 2014
6. Jun 20, 2014

### nameVoid

The book asks for a sketch I assume there is a reasonable way
Plot t values?

7. Jun 20, 2014

### Bill Simpson

Is this what you are looking for?
Code (Text):
ParametricPlot3D[{t^2, t^4, t^6}, {t, 0, 1}]
If it isn't then perhaps you can explain what is incorrect about that.

8. Jun 20, 2014

### nameVoid

Is gives a line I am under the impression that the graph is a surface
What's throwing me off is the book taking the trace in each plane
Sint,cost,t cylinder along z

9. Jun 20, 2014

### Ray Vickson

No: the point-set you describe is a one-dimensional object = a curve in 3d. If you wanted a surface you would need two independent variables, so you would need to have something like three functions x(u,v), y(u,v), z(u,v) in two variables u and v.

10. Jun 20, 2014

### nameVoid

In cost,sint,t
z for all real isn't a cylinder?

11. Jun 21, 2014

### Bill Simpson

Nope.

Code (Text):
ParametricPlot3D[{Cos[t], Sin[t], t}, {t, 0, 4 Pi}]
It is perhaps difficult to get a really good 3D view of it, but try from different angles and guess what it is.