- Thread starter
- #1

- Apr 13, 2013

- 3,723

Let the function be f(x,y)=x^2-2*y^2,which graph is S:z=f(x,y).Which are the contour curves???Are these hyperbolas???

Thanks in advance!!!!

- Thread starter evinda
- Start date

- Thread starter
- #1

- Apr 13, 2013

- 3,723

Let the function be f(x,y)=x^2-2*y^2,which graph is S:z=f(x,y).Which are the contour curves???Are these hyperbolas???

Thanks in advance!!!!

- Jan 17, 2013

- 1,667

Now , choose some values for $k$ and draw them in the xy-plane . What are these curves ?

- Thread starter
- #3

- Apr 13, 2013

- 3,723

- - - Updated - - -

Or are these hyperbolic paraboloids???

- Admin
- #4

- Mar 5, 2012

- 8,887

Heh. The

- - - Updated - - -

Or are these hyperbolic paraboloids???

The

- Thread starter
- #5

- Apr 13, 2013

- 3,723

Nice...Thank you very much!!!

- Thread starter
- #6

- Apr 13, 2013

- 3,723

- Feb 21, 2013

- 739

Regards.

- Thread starter
- #8

- Apr 13, 2013

- 3,723

Great...!!!Thank you very much...!!!

- Admin
- #9

- Mar 5, 2012

- 8,887

Well, this is a bit ambiguous.

The surface z=f(x,y) is a parametric surface in x and y.

It makes no sense to consider df/dz which would be zero, since f(x,y) does not contain z.

So I suspect you're supposed to consider g(x,y,z)=f(x,y)-z.

The equation g(x,y,z)=0 identifies the same surface.

And then yes, dg/dz=-1.

- Thread starter
- #10

- Apr 13, 2013

- 3,723

Oh good!!!!!Thank you very much!!!!

- Admin
- #11

- Mar 5, 2012

- 8,887

You're welcome!!!!!!!