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.
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.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 44E: By definition, a hyperbola is the locus of points whose positive difference of distances from two...
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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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