(722, #11) Find the traces of the surface in the planes x k, y = k, z = k.

Then identify the surface and sketch it.

Solution: The surface is an elliptic parabolid.

Rewrite the equation as . For the values y = 0.1, 1, 2, 3 we have elliptic traces:

At z = 0, , so we have the parabola:

At x = 0, , resulting in the parabola:

Bringing these results together, we have an elliptic parabolid:

Maple code

by: gm