We'll review planes (12.1) by working several examples. Then we'll turn to the more interesting quadric surfaces. We've played with several of these, including spheres, circular cylinders and cones.

As you read through section 12.1 look at the images of the surfaces. Pay attention to the curves drawn on those surfaces. These space curves are called traces, and they represent intersections between planes and the surfaces themselves. The traces help our brains interpret the images as curvy 2-dim objects living in $\mathbb{R}^3$.

Our main objective is to describe the traces with Cartesian equations and then interpret those traces as lines, circles, parabolas or hyperbolas. This is how we match a particular quadric equation with its graph. This is how we visualize surfaces.

As you read through section 12.1 look at the images of the surfaces. Pay attention to the curves drawn on those surfaces. These space curves are called traces, and they represent intersections between planes and the surfaces themselves. The traces help our brains interpret the images as curvy 2-dim objects living in $\mathbb{R}^3$.

Our main objective is to describe the traces with Cartesian equations and then interpret those traces as lines, circles, parabolas or hyperbolas. This is how we match a particular quadric equation with its graph. This is how we visualize surfaces.