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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 28E
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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.
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
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