Chapter 12 - Section 12.1 - Three-Dimensional Coordinate Systems - 12.1 Exercises: 31

A circle, $x^2+y^2 = 4$, that cuts through the z-axis at $(0,0,-1)$.

Work Step by Step

In three-space, $x^2+y^2 = 4$, is a cylinder that extends infinitely in the z-direction. What we've done here is taken a plane, $z= -1$ and "sliced" through our cylinder parallel to the xy-plane to create a 2D circle. The circle sits on the plane $z=-1$ and intercepts the z-axis at point $(0,0,-1)$.

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