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.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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Question
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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