# Math Help - Parametrize the curve of intersection

1. ## Parametrize the curve of intersection

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.

2. Originally Posted by jonnyp2009
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 $z^2$ to get

$z^2=\frac{1-x^2}{2}$

sub this into the first equation to get

$x^2+y^2+\frac{1}{2}-\frac{x^2}{2}=1$

$\frac{x^2}{2}+y^2=\frac{1}{2} \iff x^2+\frac{y^2}{(\frac{1}{\sqrt{2}})^2}=1$

This is an equation of an ellipse...

This should get you started

3. ok thanks i got it now, i then get x=cost and solve for y then plug them both into sphere equation for z

so $y=1/sqrt(2)sint$
and $z=1/sqrt(2)sint$