I need to find the points on:

$\displaystyle x^2+\frac{y^2}{4}+\frac{z^2}{9}=1$

where the tangent line is parallel to:

$\displaystyle x+2y+z=0$

This is what I've done:

$\displaystyle \langle 2x, \frac{y}{4}, \frac{2z}{9} \rangle \cdot \langle 1,2,1 \rangle =0$

$\displaystyle =2x+y+\frac{2z}{9}=0$

Not sure what to do now... do I have to change this to parametric form? Should I have changed it first?