2. Given: surface Q : 9x2 – 422 = 9y(a) Give the equation of the trace of Q on each coordinate plane andon the planes y4 and y-4. Identify each trace.(b) Identify the quadric surface and sketch the graph of Q. Label allimportant points on the traces.

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Answered: 2. Given: surface Q : 9x² – 42² = 9y -…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Analytic Trigonometry

Section2.3: Solving Trigonometric Equations

Problem 11ECP

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Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
Given the surface 9x^2 − 4z^2 = 9y. Find its traces on each coordinate plane and on the planes y=4, y=-4. Give the vertices and sample points of the parabolas and hyperbolas formed.
By hand, without any graphical utilities, sketch the following surface: z = x2 - (y2 / 4)
Consider the following surface: z = x2 - (y2 / 4). By hand, without any graphical utilities, find an equation for the intersection of the surface and a plane containing the points (1, 0, 0), (2, 4, 0), and (-1, -1, -1).
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Given the surface 9x^2 − 4z^2 = 9y. 1. Find its traces on each coordinate plane and on the planes y=4, y=-4. 2. Give the vertices and co-vertices of the hyperbolas formed. 3. Give vertices and sample points of the parabolas formed.
Show the complete solution for the following problems.Let S be the surface with equation given by 4x2- 9y2 = 9(z2 + 4).I. Find an equation of the trace of S on each of the coordinate planes and on the planes x = ±3√ 2. Determine if each trace is empty, a point, a (pair of) line(s), a parabola, an ellipse, or a hyperbola.II. What type of quadric surface is S?III. Using the traces obtained in I, provide a hand-drawn sketch of S. Label all important points (e.g. vertices) found on each trace.IV. View S as a surface of revolution. Find an equation of a generating curve on the xy-plane which, if revolved about the x-axis, will result to S.

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2. Given: surface Q : 9x² – 42² = 9y - (a) Give the equation of the trace of Q on each coordinate plane and on the planes y 4 and y –4. Identify each trace. || || (b) Identify the quadric surface and sketch the graph of Q. Label all important points on the traces.