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given line and pass through a given plane (b) The equation of the graph above is given by I= sin z (0)y + sin z The %3D surface of the equation is generated by the black curve above x= sin z. All red lines above are parallel to the y-axis. second-degree equation in three variables

given line and pass through a given plane (b) The equation of the graph above is given by I= sin z (0)y + sin z The %3D surface of the equation is generated by the black curve above x= sin z. All red lines above are parallel to the y-axis. second-degree equation in three variables

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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See the picture For the right one, it said that x=sin z=(0)y+sin z. What is the meaning of (0)y? Does the y-axis spread endlessly like the other two examples?
Lecture Notes 4: Cylinders and Quadric Surfaces A cylinder is a surface that consists of all lines (called rulings) that are parallel to a given line and pass through a given plane curve. 三1 ZA y = x2 y ( Eliptic.cylinder (b) The graph of equation y = x is called a parabolic horizontal cross-sections are parallel The graph of equation below The equation of the graph above is given by surface of the equation is generated by cylinder because the x = sin z = (0)y + sin z The parabolas. The parabolic cylinder above is called an elliptic cylinder because the the black curve above x = sin z. All red extends itself upwards and downwards horizontal cross-sections are parallel lines above are parallel to the y-axis. ellipses (distorted circles). The cylinder above extends itself upwards and downwards endlessly in 3-space. endlessly in 3-space. We will then move to see some quadric surfaces. A quadric surface is the graph of a second-degree equation in three variables X,y, z.The most general such equation is given by Ax2 + By2 + Cz2 + Dxy + Eyz + Fxz + Gx + Hy + Iz +J=0,
Transcribed Image Text:Lecture Notes 4: Cylinders and Quadric Surfaces A cylinder is a surface that consists of all lines (called rulings) that are parallel to a given line and pass through a given plane curve. 三1 ZA y = x2 y ( Eliptic.cylinder (b) The graph of equation y = x is called a parabolic horizontal cross-sections are parallel The graph of equation below The equation of the graph above is given by surface of the equation is generated by cylinder because the x = sin z = (0)y + sin z The parabolas. The parabolic cylinder above is called an elliptic cylinder because the the black curve above x = sin z. All red extends itself upwards and downwards horizontal cross-sections are parallel lines above are parallel to the y-axis. ellipses (distorted circles). The cylinder above extends itself upwards and downwards endlessly in 3-space. endlessly in 3-space. We will then move to see some quadric surfaces. A quadric surface is the graph of a second-degree equation in three variables X,y, z.The most general such equation is given by Ax2 + By2 + Cz2 + Dxy + Eyz + Fxz + Gx + Hy + Iz +J=0,
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