(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a vector function that parameterizes a curve C which lies in the plane x-y+z=2 and directly above the circle x^{2}+ (y-1)^{2}= 9

3. The attempt at a solutionSo, in order to parameterize the circle, I simply use x=cos(t), y = sin(t) with some adjustments. Namely, I let x=3cos(t) and y=3sin(t)+1. Then, to determine how the z-coordinates of this curve change according to x,y I use the definition of the plane. So I have z=2-x+y, which I convert using my parametric defintions for x,y.

I have, z=3-3cos(t)+3sin(t). Therefore, my parameterized curve is,

<3cos(t),3sin(t)+1,3-3cos(t)+3sin(t)>

Right?

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# Parameterizing A Circle Projected onto a Plane

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