Find the Vector function that represents the curve of the intersection of the two surfaces.  The Semiellipsoid x^2+y^2+4z^2=4, y is more than 0, and the cylinder x^2+z^2=1

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the Vector function that represents the curve of the intersection of the two surfaces. 

The Semiellipsoid x^2+y^2+4z^2=4, y is more than 0, and the cylinder x^2+z^2=1 

Expert Solution
Step 1

Given equations are

x2+y2+4z2=4 ..... (1)

and x2+z2=1 ..... (2)

From equation (1)

z2=(4-x2-y2)/4 ..... (3)

From equation (2)

z2=1-x2 ..... (4)

From equations (3) and (4)

4-x2-y2=4(1-x2)

4-x2-y2=4-4x2

3x2=y2

x=y3..... (5)

 

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