Parametrization of Intersection.

Have no idea how to solve this problem.

Problem:

Parameterize the curve of the intersection of the surfaces $\displaystyle x^2+y^2=9$ 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.

Re: Parametrization of Intersection.

Quote:

Originally Posted by

**Bracketology** Have no idea how to solve this problem.

Problem:

Parameterize the curve of the intersection of the surfaces $\displaystyle x^2+y^2=9$ 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.

Re: Parametrization of Intersection.

Quote:

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!