Sec10.6 - Sec.10.6 Cylinders and Quadric Surfaces Sketches:...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Sec.10.6 Cylinders and Quadric Surfaces Sketches: To sketch a surface it is useful to find the traces of cross-sections where the planes passing through the surface are parallel to the coordinated planes. A cylinder is a surface that consist of all lines (rulings) parallel to a given line and passing through a given plane curve (generating curve). If one of the variables x y, or z is missing from the equation of a surface, then the surface is a cylinder. EX1 Sketch the graph of the surfaces below. A. z = y 2 B. x 2 + z = 1 A quadric surface is the graph of a second degree equation in 3 variables say x, y, and z. Quadratic surfaces are the 3D counter part of conic sections in 2D. (See table on page 655 of text.) Ellipsoid All three traces are ellipses. 222 1 xyz abc + += If a = b = c > 0, we have a sphere. EX 2 Sketch 4x 2 + 9y 2 + 36z 2 = 36
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Elliptic paraboloid For the first formula, horizontal traces are ellipses; vertical traces are parabolas.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/28/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

Page1 / 4

Sec10.6 - Sec.10.6 Cylinders and Quadric Surfaces Sketches:...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online