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- Mar 21st 2008, 07:18 PM #1

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- Sep 2007
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- 94

## Am I doing this right?

Find a vector function that represents the curve of intersection of the two surfaces.

The cylinder x^2 + y^2 = 4 and the surface z = xy.

What I do is make z = 0, then x^2 + y^2 = 4 is a circle and

xy = 0.

Then I make these equations equal each other.

x^2 + y^2 - 4 = xy and simplify

x^2 + y^2 - xy - 4 = 0

But now I can't seem to complete the square.

Any help would be appreciated.

- Mar 21st 2008, 08:06 PM #2

- Mar 21st 2008, 08:20 PM #3

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- Sep 2007
- Posts
- 94

I'm setting z = 0 to simplify the expression so I can complete the square. It appears that this is not the way to go. Could you write out in mathematical terms the rotation about the z - axis here for me please. I guess when you deal with surfaces its not the same as curves.

- Mar 22nd 2008, 04:01 AM #4
It's easier than you think:

The curve is the set of points that satisfy and . Using parametric equations:

To satisfy , and (note: clearly other choices are possible).

Therefore, to satisfy it is required that .

Note that .

Therefore the vector equation of the curve is:

, where .

- Mar 22nd 2008, 05:02 AM #5