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Cylinders and Quadratic Surfaces

Cylinders and Quadratic Surfaces. A cylinder is the continuation of a 2-D curve into 3-D. No longer just a soda can. Ex. Sketch the surface z = x 2. Ex. Sketch the surface y 2 + z 2 = 1. A quadratic surface has a second-degree equation. The general equation is:

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Cylinders and Quadratic Surfaces

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  1. Cylinders and Quadratic Surfaces A cylinder is the continuation of a 2-D curve into 3-D. No longer just a soda can. Ex. Sketch the surface z = x2.

  2. Ex. Sketch the surface y2 + z2 = 1.

  3. A quadratic surface has a second-degree equation. The general equation is: A trace is the intersection of a surface with a plane. We will use the traces of the quadratic surfaces with the coordinate planes to identify the surface.

  4. Ex Sketch the surface xy-trace yz-trace xz-trace The Graph

  5. Ex Sketch the surface xy-trace yz-trace xz-trace The Graph

  6. Ex Sketch the surface xy-trace yz-trace xz-trace The Graph

  7. Ex Sketch the surface xy-trace yz-trace xz-trace The Graph

  8. Ex Sketch the surface xy-trace yz-trace xz-trace The Graph

  9. Ex Sketch the surface -trace -trace -trace The Graph

  10. Ex Determine the region bounded by and x2 + y2 + z2 = 1 xy-trace yz-trace xz-trace The Graph

  11. Surfaces of rotation x-axis: y2 + z2 = [r(x)]2 y-axis: x2 + z2 = [r(y)]2 z-axis: x2 + y2 = [r(z)]2 Ex. Write the equation of the surface generated by revolving about the y-axis.

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