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Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface given by the equation.

Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface given by the equation.

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter8: Analytic Geometry
Section8.4: Rotation Of Axis
Problem 1SE: What effect does the xyterm have on the graph of a conic section?
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Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface given by the equation. O.
Transcribed Image Text:Consider the equation of the surface. 1 f (x, y) = x² + y² + 1 Identify the graph of the surface given by the equation. O.
Identify the traces. The horizontal trace at height c is a circle in the plane z = c for 0 < c < 1, The horizontal trace at height c is the origin in the plane z = c for c = 1. The vertical trace in the plane x = a is a parabola for all a. The vertical trace in the plane y = a is the curve z = x² + a² + 1 The vertical trace in the plane x = c is a circle for all c. Incorrect 口口 口 口
Transcribed Image Text:Identify the traces. The horizontal trace at height c is a circle in the plane z = c for 0 < c < 1, The horizontal trace at height c is the origin in the plane z = c for c = 1. The vertical trace in the plane x = a is a parabola for all a. The vertical trace in the plane y = a is the curve z = x² + a² + 1 The vertical trace in the plane x = c is a circle for all c. Incorrect 口口 口 口
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