Parametric representation of a surface

[Pete_01]

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?

 

[Dick]

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?

 

[Pete_01]

How did you know to make the equation into x/2 instead of 2x? Is it really x/r in effect?

 

[Dick]

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.

 

[Pete_01]

Oh ok gotcha, great help thanks!