Math Help - sketching circle/sphere - multivariable calculus question

1. sketching circle/sphere - multivariable calculus question

hi everyone, i'm having some trouble sketching this function:

3x^2 + 2y^2 = 1

my problem is that ive found the x and y intercepts, but can't seem to find how it connects together to make a cylinder...

i got these as the intercepts, both + and - values:

x = square root [ (1-2y^2) divided by 3 ]
y = square root [ (1-3y^2) divided by 2 ]

thanks!

2. $3x^2 + 2y^2 = 1$ is an ellipse on a 2 dimensional plane.
where as on 3 dimensional plane its a cylinder