# [SOLVED] intersection between cylinder &amp; plane

• Sep 23rd 2009, 04:36 PM
snaes
[SOLVED] intersection between cylinder &amp; plane
Find a vector function that represents the curve of intersection of the cylinder $x^2+y^2=16$ and plane $x+z=5.$

I am stuck. I setting the equation equal to eachother but i could not solve for anything or get anything useful out of it.

I believe I am supposed to project the cylinder down so its a circle on the xy plane and then find the ellipse that the intersecion makes but i cannot figure out how.

Any help would be appreciated.
• Sep 23rd 2009, 05:02 PM
redsoxfan325
Quote:

Originally Posted by snaes
Find a vector function that represents the curve of intersection of the cylinder $x^2+y^2=16$ and plane $x+z=5.$

I am stuck. I setting the equation equal to eachother but i could not solve for anything or get anything useful out of it.

I believe I am supposed to project the cylinder down so its a circle on the xy plane and then find the ellipse that the intersecion makes but i cannot figure out how.

Any help would be appreciated.

I would solve for each variable in terms of $x$.

$x=x$
$y=\pm\sqrt{16-x^2}$
$z=5-x$

Let x=t and now you have the vector function

$\left\langle t,\pm\sqrt{16-t^2},5-t\right\rangle$, $-4\leq t\leq 4$
• Sep 23rd 2009, 06:55 PM
snaes
Thanks for trying. :)
• Sep 23rd 2009, 06:57 PM
redsoxfan325
Trying? Is that not the right answer?
• Sep 24th 2009, 09:48 AM
snaes
Ah yes its in a different form. The form i was looking at had sin(x) which when converted would work out. Thank!
• Sep 24th 2009, 10:43 AM
redsoxfan325
Quote:

Originally Posted by snaes
Ah yes its in a different form. The form i was looking at had sin(x) which when converted would work out. Thank!

It was probably in polar. Something like:

$\langle 4\cos\theta,4\sin\theta,5-4\cos\theta\rangle$ for $0\leq\theta<2\pi$