1)² y² Consider the surface S₂ with equation 4 a) Find an equation of the trace of S₂ on the xy-plane, the xz-plane, the plane x = 1, and the planes z = ±3. Identify the type of conic each trace represents. - 9 3 = 1. b) What type of quadric surface is S₂? c) Sketch the graph of S₂ using the traces obtained in 3.a). Label all important points found on each trace.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 19RE
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Question
Consider the surface S₂ with equation
(x - 1)² y² 22
9 3
+
4
a) Find an equation of the trace of S₂ on the xy-plane, the xz-plane, the plane x = 1, and the
planes z = 13. Identify the type of conic each trace represents.
b) What type of quadric surface is S₂?
c) Sketch the graph of S₂ using the traces obtained in 3.a). Label all important points found on
each trace.
-
= 1.
Transcribed Image Text:Consider the surface S₂ with equation (x - 1)² y² 22 9 3 + 4 a) Find an equation of the trace of S₂ on the xy-plane, the xz-plane, the plane x = 1, and the planes z = 13. Identify the type of conic each trace represents. b) What type of quadric surface is S₂? c) Sketch the graph of S₂ using the traces obtained in 3.a). Label all important points found on each trace. - = 1.
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