# Thread: [SOLVED] intersection between cylinder &amp; plane

1. ## [SOLVED] intersection between cylinder &amp; plane

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

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.

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

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 $\displaystyle x$.

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

Let x=t and now you have the vector function

$\displaystyle \left\langle t,\pm\sqrt{16-t^2},5-t\right\rangle$, $\displaystyle -4\leq t\leq 4$

3. Thanks for trying.

4. Trying? Is that not the right answer?

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

6. 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:

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