Quick parametric equation question

[fball558]

Homework Statement

Find a parametric representation for the lower half of the ellipsoid 3x^2 + 5y^2 + z^2 = 1
x=u
y=v

z=??

we need to find what z is

The Attempt at a Solution

i solved the equation for z getting

z= sqrt(1-3x^2-5y^2)

then i plugged the given x=u and y=v into equation
to get
z= sqrt(1-3u^2-5v^2)

but that is wrong?
what should i do instead??

 

[lanedance]

Homework Statement

Find a parametric representation for the lower half of the ellipsoid 3x^2 + 5y^2 + z^2 = 1
x=u
y=v

z=??

we need to find what z is

The Attempt at a Solution

i solved the equation for z getting

z= sqrt(1-3x^2-5y^2)

then i plugged the given x=u and y=v into equation
to get
z= sqrt(1-3u^2-5v^2)

but that is wrong?
what should i do instead??

shouldn't z be negtive for the lower half?

 

[fball558]

:( yes... i need to learn how to read.
thanks a lot lanedance
that is right :)

 

[HallsofIvy]

Did the problem specifically say that you must use x and y themselves as parameters? There is enough "symmetry" here that I would have use "modified" spherical coordinates:
[tex]x= \frac{\sqrt{3}}{3}cos(\theta)sin(\phi)[tex]
[tex]y= \frac{\sqrt{5}}{5}sin(\theta)sin(\phi)[tex]
[tex]z= cos(\phi)[/tex]
with [itex]0\le \theta< 2\pi[/itex] and [itex]\pi/2 \le \phi \le \pi[/itex].