# Math Help - Parametrization of Intersection.

1. ## Parametrization of Intersection.

Have no idea how to solve this problem.

Problem:
Parameterize the curve of the intersection of the surfaces $x^2+y^2=9$ and z=x+2y the point (3,0,3) should correspond to the point t=0.

The first equation is a circle of radius 3. So I know that paramterization should be
x=3sin(t*pi)
y=3cos(t*pi)

No idea how to solve for the intersection of the two though.

2. ## Re: Parametrization of Intersection.

Originally Posted by Bracketology
Have no idea how to solve this problem.

Problem:
Parameterize the curve of the intersection of the surfaces $x^2+y^2=9$ and z=x+2y the point (3,0,3) should correspond to the point t=0.

The first equation is a circle of radius 3. So I know that paramterization should be
x=3sin(t*pi)
y=3cos(t*pi)

No idea how to solve for the intersection of the two though.
Since the point (3,0,3) should correspond to the point t=0, it should be

x=3cos(t*pi)
y=3sin(t*pi)

in which case

z=3cos(t*pi) + 6sin(t*pi)

and that's the answer. Think about it.

3. ## Re: Parametrization of Intersection.

Originally Posted by mr fantastic
Since the point (3,0,3) should correspond to the point t=0, it should be

x=3cos(t*pi)
y=3sin(t*pi)

in which case

z=3cos(t*pi) + 6sin(t*pi)

and that's the answer. Think about it.

That's it? Seems simple. I just haven't gotten the hang of parametrics yet. Luckily its another 6 weeks before our next test, so that gives me plenty time to learn. Thanks for the help!