   Chapter 12.1, Problem 54E

Chapter
Section
Textbook Problem

# Representing a Graph by Vector-Valued Function In exercises 55-62 sketch the space curve represented by the intersection of the surfaces a. Then represent the curve by a vector valued function using the given parameter.Surfaces Parameter z = x 2 + y 2 , z = 4 x = 2 cos t

To determine

To graph: The space curve represented by the intersection of the surface and represent the curve by a vector valued function.

Explanation

Given: Surface z=x2+y2,z=4 and parameter x=2cost.

Graph: Red coloured curve is the required curve of intersection (done by mathematica)

Interpretation: The intersection of curve is represented by r(t)=2costi+2sintj+4k.

Given 4=(2cost)2+y2y2=44cos2t=4(1cos2t)=4sin2ty=4sin2t

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