Explanation Given info. x 2 + y 2 = z 2 Concept used: Equation of circle in x y plane x 2 + y 2 = R 2 , whose parametric form is ( R cos θ , R sin θ ) . With the help of this you can write parametric form. Calculation. x 2 + y 2 = z 2 ( comparison To determine (b) Use this to be a parameterization of Viviane’s curve with θ as parameter I.e. intersection of x 2 + y 2 = z 2 , y = z 2 .

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 14.1, Problem 32E

To determine

(a)

Show that any point on $x^{2} + y^{2} = z^{2}$ can be written in the form $(z \cos θ, z \sin θ, z)$ for some $θ$ .

To determine

(b)

Use this to be a parameterization of Viviane’s curve with $θ$ as parameter I.e. intersection of $x^{2} + y^{2} = z^{2}, y = z^{2}$ .

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Chapter 14.1, Problem 31E

Chapter 14.1, Problem 33E

Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY

(a) Show that any point on x 2 + y 2 = z 2 can be written in the form ( z cos θ , z sin θ , z ) for some θ .

Solution Summary: The author explains that any point on x 2 + y 2 = z 2 can be written in the form for some.

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(a)

Show that any point on $x^{2} + y^{2} = z^{2}$ can be written in the form $(z \cos θ, z \sin θ, z)$ for some $θ$ .

(b)

Use this to be a parameterization of Viviane’s curve with $θ$ as parameter I.e. intersection of $x^{2} + y^{2} = z^{2}, y = z^{2}$ .

Want to see the full answer?

Chapter 14 Solutions

(a) Show that any point on x 2 + y 2 = z 2 can be written in the form ( z cos θ , z sin θ , z ) for some θ .

Solution Summary: The author explains that any point on x 2 + y 2 = z 2 can be written in the form for some.

Concept explainers

Videos

(a) Show that any point on x2+y2=z2 can be written in the form (zcosθ,zsinθ,z) for some θ.

(b) Use this to be a parameterization of Viviane’s curve with θ as parameter I.e. intersection of x2+y2=z2,y=z2.

Want to see the full answer?

Chapter 14 Solutions

(a)

Show that any point on $x^{2} + y^{2} = z^{2}$ can be written in the form $(z \cos θ, z \sin θ, z)$ for some $θ$ .

(b)

Use this to be a parameterization of Viviane’s curve with $θ$ as parameter I.e. intersection of $x^{2} + y^{2} = z^{2}, y = z^{2}$ .