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 arehyperbolas.

If is positive, the hyperbola is "vertical":

If is negative, the hyperbola is "horizontal":

If , we have a pair of intersecting lines: