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Describe the following surfaces and give traces where available:

1. 16x^2 + 16y^2 - 9z^2 = 0

2. y = 2z

1. This can be rewritten as 16x² + 16y² = 9z².

For any value of z, this is the equation of a circle with radius 3z.

This looks like it would be a cone below and above the origin,

with a single point at the origin.

Both above and below, it would widen forever in a linear fashion.

2. In the y-z plane, this is a line.

When x is thrown in, it makes a plane that slopes just like the line does.

That is, the plane has slope to in the y direction with respect to z

and at each point (y,z) on the plane, x can take on any value.

Calculus

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