Parameterization of 9x^2 + 6y^2 + z^2 = 1, an ellipsoid

[MarkSA]

Hello,

I have the following problem:
Find the parametric representation of the quadric surface, which is an ellipsoid:
9x^2 + 4y^2 +z^2 = 1

All it is asking for is to convert this into a parametric equation. But i'm having trouble figuring out how to do this.
I thought I could set two variables equal to zero to find out the radius of each section of the ellipse. I did:
9x^2 = 1. x = +/- 1/3
and
4y^2 = 1. y = +/- 1/2
and
z^2 = 1, z = +/- 1

But at this point i'm not sure how to take that and make a parametric equation out of it in terms of two variables (u,v).

 

[Unco]

Hi Mark,

Recall that a parameterisation of the circle x^2+y^2=1 is (x, y) = (cos(t), sin(t)). We could then use this to parameterise the ellipse (x/a)^2 + (y/b)^2 = 1: putting x/a = cos(t) and y/b = sin(t); hence (x,y) = (acos(t), bsin(t)).

Similarly we may parameterise an ellipsoid using a parameterisation of a sphere. Are you familiar with spherical coordinates? If not, look in your text or google.

 

[MarkSA]

I know spherical but i'm not really sure how to apply it to this problem.

Is it possible to parameterize this using rectangular? That's what I tried originally. I was ending up with
x=x
y=y
z=sqrt(1-4*y^2-9x^2)

That's a method I saw used on a different problem, but it wasn't for an ellipsoid. If I graph this to check my answer I get the general shape of the ellipsoid but half of it is missing and the edges are jagged (that may be due to the CAS I am using)