Consider the following equation of a quadric surface 9x^2 - 81y^2 - (z^2/4)=0 (a) Find the intercepts with the three coordinate axes, when they exist. (b) Find the equations (and describe them in words) of the xy−, xz−, and yz− traces, when they exist. (c) Identify (by name) and sketch a graph of the surface.
Consider the following equation of a quadric surface 9x^2 - 81y^2 - (z^2/4)=0 (a) Find the intercepts with the three coordinate axes, when they exist. (b) Find the equations (and describe them in words) of the xy−, xz−, and yz− traces, when they exist. (c) Identify (by name) and sketch a graph of the surface.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following equation of a quadric surface
9x^2 - 81y^2 - (z^2/4)=0
(a) Find the intercepts with the three coordinate axes, when they exist.
(b) Find the equations (and describe them in words) of the xy−, xz−, and yz− traces, when they exist.
(c) Identify (by name) and sketch a graph of the surface.
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Why are 9x^2-81y^2=0 and 9x^2-(z^2/4)=0 hyperbolas that pass through the origin and not lines that intersect at the origin?
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