Calculus › Section L · Vectors and the geometry of space › Topic L.6
Surfaces in space
One equation in three variables draws not a curve but a surface, and a surface cannot be seen all at once. Slicing it with planes, the way a scanner slices a body, turns every 3-D shape into a family of familiar 2-D curves.
In this topic
- Drawing the invisible
- Traces
- Cylinders: the missing variable
- Quadric surfaces: the second-degree family
- Paraboloids: the first-power tell
- Worked example: classifying a hyperboloid
- Worked example: a quadric away from the origin
- Surfaces of revolution
- Surfaces at work
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP