# Where does the plane intersect the curve?

• Oct 25th 2012, 06:20 PM
Where does the plane intersect the curve?
Find the point(s) where the following plane and curve intersect:
2x+3y-9z=0
r(t)= <3cost, 3sint, cost> for [0,2pi]
• Oct 25th 2012, 07:21 PM
TheEmptySet
Re: Where does the plane intersect the curve?
Quote:

$6\cos(t)+9\sin(t)-9\cos(t)=0 \iff 9\sin(t)=3\cos(t) \iff \tan(t)=\frac{1}{3}$
$t=\tan^{-1}\left( \frac{1}{3}\right)+\pi n, n \in \mathbb{Z}$