# Thread: Parametrizing the Intersection of Surfaces

1. ## Parametrizing the Intersection of Surfaces

Hello, I am stuck on this problem involving the parametrizing of two surfaces :

Find a parametrization of the following curve:
The intersection of the plane with the sphere

$r(t)= < ? , 7 , ?>$

I have gotten the second component which is simply 7, but that's as far as i have gotten, i know that the first and third are going to involve cos(t) and sin(t) respectivly, but how do i go about solving them?

Thanks again!!

2. Originally Posted by Esc
Hello, I am stuck on this problem involving the parametrizing of two surfaces :

Find a parametrization of the following curve:
The intersection of the plane with the sphere

$r(t)= < ? , 7 , ?>$

I have gotten the second component which is simply 7, but that's as far as i have gotten, i know that the first and third are going to involve cos(t) and sin(t) respectivly, but how do i go about solving them?

Thanks again!!
plug in y = 7 in the sphere and solve. you get $x^2 + z^2 = 5^2$ .......this is a circle of radius 5, how do we parameterize circles?

3. Originally Posted by Jhevon
plug in y = 7 in the sphere and solve. you get $x^2 + z^2 = 5^2$ .......this is a circle of radius 5, how do we parameterize circles?
i know that $x^2 + z^2=5^2$ is going to equal $sin^2(x) + cos^2(x)=5^2$ and i found the answer to be $<5cos(t), 7, 5sin(t)>$ and it was corect!!!!

Thank you soooo much!!!!

4. Originally Posted by Esc
i know that $x^2 + z^2=5^2$ is going to equal $sin^2(x) + cos^2(x)=5^2$ and i found the answer to be $<5cos(t), 7, 5sin(t)>$ and it was corect!!!!

Thank you soooo much!!!!
very good!