Parametric representation of a surface

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Homework Help Overview

The discussion revolves around expressing a surface defined by parametric equations in the form of a level surface function f(x,y,z) = 144. The subject area includes parametric representations and level surfaces in three-dimensional geometry.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the transformation of parametric equations into a level surface equation. Questions arise regarding the manipulation of the equations and the reasoning behind specific algebraic steps.

Discussion Status

Some participants have offered insights into the structure of the level surface equation, while others are questioning the rationale behind certain transformations. There is an ongoing exploration of different interpretations of the problem.

Contextual Notes

Participants are discussing the implications of constants in the parametric equations and how they affect the formulation of the level surface. There is a lack of consensus on the best approach to derive f(x,y,z).

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Homework Statement


Express the surface
x = 2cos(theta)sin(phi) y=3sin(theta)sin(phi) z=2cos(phi)
as a level surface f(x,y,z) = 144,
f(x,y,z) = ?


Homework Equations





The Attempt at a Solution


I figured they wanted the equation f(x,y,z) in x^2+y^2+z^2=144 so I though that by making the r's in the equations the same that would be the way to go.--> 24x^2+36y^2+24y^2 = 144 Where am I going wrong?
 
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Looks to me like (x/2)^2+(y/3)^2+(z/2)^2=1. Do you agree? Now how about a form for f(x,y,z)=144?
 
How did you know to make the equation into x/2 instead of 2x? Is it really x/r in effect?
 
Because I know if x=cos(theta)sin(phi) y=sin(theta)sin(phi) z=cos(phi) then x^2+y^2+z^2=1. I just divided off the constants.
 
Oh ok gotcha, great help thanks!
 

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