For the surface defined by z^2 = x^3+2xy^2-x, describe as best you can the traces in planes parallel to the yz-plane.

Please teach me how to do this question. Thank you very much.

Results 1 to 2 of 2

- January 15th 2007, 04:27 PM #1

- Joined
- Nov 2006
- Posts
- 123

- January 15th 2007, 05:08 PM #2

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 11,976
- Thanks
- 812

Hello, Jenny!

For the surface defined by ,

describe as best you can the traces in planes parallel to the yz-plane.

A plane parallel to the yz-plane has the equation: . (constant).

In the equation let

. . So we have: .

is a constant; call it .

is a constant; call it .

The equation has the form: .

The traces are*hyperbolas.*

If is positive, the hyperbola is "vertical":

If is negative, the hyperbola is "horizontal":

If , we have a pair of intersecting lines: