# Thread: Curve of intersection of the surfaces

1. ## Curve of intersection of the surfaces

Show that the curve with vector equation is the curve of intersection of the surfaces $(x-1)^2+y^2 = 1$ and $x^2 + y^2 + z^2 = 4$. Use this fact to sketch the curve.

I am completely lost.

Would i take $z = 2sin(t)$ and plug it into

$x^2 + y^2 + z^2 = 4$

$x^2 + y^2 + (2sin(t))^2 = 4$
then
$x^2 + y^2 + (4sin^2(t)) = 4$

I dont know what to do.

2. ## Re: Curve of intersection of the surfaces

Oh, nevermind i think i got it. I solve for y^2 and plug that into the surface.