# Parametrization of Intersection.

• Oct 2nd 2011, 06:01 PM
Bracketology
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.
• Oct 2nd 2011, 08:14 PM
mr fantastic
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 $x^2+y^2=9$ 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)

• Oct 2nd 2011, 08:25 PM
Bracketology
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)