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.

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- Jan 15th 2007, 05:27 PMJenny20z^2 = x^3+2xy^2-x
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. - Jan 15th 2007, 06:08 PMSoroban
Hello, Jenny!

Quote:

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: