Section 13.1 is a difficult read, but try to get a sense for what it covers and for the questions you'll be asked.

We've seen lines and curves in space that lie at the intersection of two surfaces, and we know how to write parametric equations for lines in space. Now, we'll parametrize a variety of space curves by starting with the Cartesian equations that describe those curves. We'll also create parametrizations out of thin air and then try to decide which surfaces the space curves lie on.

We've seen lines and curves in space that lie at the intersection of two surfaces, and we know how to write parametric equations for lines in space. Now, we'll parametrize a variety of space curves by starting with the Cartesian equations that describe those curves. We'll also create parametrizations out of thin air and then try to decide which surfaces the space curves lie on.