Parametrize the curve of intersection of the sphere x^2+y^2+z^2=1 and the elliptic cylinder x^2+2z^2=1. Find the total length of this intersection curve.
Note you can solve the 2nd equation for $\displaystyle z^2$ to get
$\displaystyle z^2=\frac{1-x^2}{2}$
sub this into the first equation to get
$\displaystyle x^2+y^2+\frac{1}{2}-\frac{x^2}{2}=1$
$\displaystyle \frac{x^2}{2}+y^2=\frac{1}{2} \iff x^2+\frac{y^2}{(\frac{1}{\sqrt{2}})^2}=1$
This is an equation of an ellipse...
This should get you started