(a) Find and identify the traces of the quadric surface x2 + y2 − z2 = 81 given the plane. x = k Find the trace. Identify the trace. circleellipse hyperbolaparabola y = k Find the trace. Identify the trace. circleellipse hyperbolaparabola z = k Find the trace. Identify the trace. circleellipse hyperbolaparabola Describe the surface from one of the graphs in the table. ellipsoidelliptic paraboloid hyperbolic paraboloidconehyperboloid of one sheethyperboloid of two sheets
(a) Find and identify the traces of the quadric surface x2 + y2 − z2 = 81 given the plane. x = k Find the trace. Identify the trace. circleellipse hyperbolaparabola y = k Find the trace. Identify the trace. circleellipse hyperbolaparabola z = k Find the trace. Identify the trace. circleellipse hyperbolaparabola Describe the surface from one of the graphs in the table. ellipsoidelliptic paraboloid hyperbolic paraboloidconehyperboloid of one sheethyperboloid of two sheets
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 35E
Related questions
Question
(a) Find and identify the traces of the quadric surface
x2 + y2 − z2 = 81
given the plane.
x = k
Find the trace.
Identify the trace.
Identify the trace.
circleellipse hyperbolaparabola
y = k
Find the trace.
Identify the trace.
Identify the trace.
circleellipse hyperbolaparabola
z = k
Find the trace.
Identify the trace.
Identify the trace.
circleellipse hyperbolaparabola
Describe the surface from one of the graphs in the table.
ellipsoidelliptic paraboloid hyperbolic paraboloidconehyperboloid of one sheethyperboloid of two sheets
(b) If we change the equation in part (a) to
x2 − y2 + z2 = 81,
how is the graph affected?
The graph is rotated so that its axis is the x-axis.The graph is rotated so that its axis is the y-axis. The graph is rotated so that its axis is the z-axisThe graph is shifted one unit in the negative y-direction.The graph is shifted one unit in the positive y-direction.
(c) What if we change the equation in part (a) to
x2 + y2 + 2y − z2 = 80?
The graph is rotated so that its axis is the x-axis.The graph is rotated so that its axis is the y-axis. The graph is rotated so that its axis is the z-axisThe graph is shifted one unit in the negative y-direction.The graph is shifted one unit in the positive y-direction.
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