M310 L05 12'6 Cylinders and Quadric Surfaces

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M310 L05 12.6 Cylinders and Quadric Surfaces

• Traces, Cylinders, and Rulings
• 1 Sketching a Parabolic Cylinder
• 2 Two Circular Cylinders
• 3 Use Traces to Sketch an Ellipsoid
• 4 Use Traces to Sketch an Elliptic Paraboloid
• 5 Use Traces to Sketch a Hyperbolic Paraboloid
• 6 Use Traces to Sketch a Hyperboloid of One
  Sheet
• 7 Use Traces to Sketch a Hyperboloid of Two
  Sheets
• 8 Use Traces to Classify a Surface

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12.6 1 Sketching a Parabolic Cylinder
To sketch the graph of yx2, we first notice z
is missing, and then examine various
cross-sections.
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12.6 2 Sketching Circular Cylinders
Identify and sketch the surfaces represented by
the following equations.
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12.6 3 Sketching an Ellipsoid
Identify and sketch the surface represented by
the following equation. (Use traces.)
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12.6 4 Sketching an Elliptic Paraboloid
Identify and sketch the surface represented by
the following equation. (Use traces.)
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12.6 5 Sketching a Hyperbolic Parab
Identify and sketch the surface represented by
the following equation. (Use traces.)
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12.6 6 Sketch Hyperboloid of One Sheet
Identify and sketch the surface represented by
the following equation. (Use traces.)
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12.6 7 Sketch Hyperboloidof TwoSheets
Identify and sketch the surface represented by
the following equation. (Use traces.)
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12.6 8 Classify a Surface
Identify and sketch the surface represented by
the following equation. (Use traces.)
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12.6 ? Cone
A clear discussion requires cylindrical
coordinates