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August 10th, 2017, 06:18 AM   #1
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parameterization of curve

I wonder whether this is correct because later, when trying to find the osculating circle, I get huge numbers and a lot of roots.

x^2+y^2-z^2=1

x+y+z=0

Trying to parametrize this, I got:

z=-x-y
x^2+y^2-(-x-y)^2=1
x^2+y^2-(x^2+2xy+y^2)=1
-2xy=1
xy=-1/2

So: x=t
y=-1/2t
z=(-2t^2+1)/2t

Last edited by skipjack; August 10th, 2017 at 07:22 AM.
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August 10th, 2017, 07:31 AM   #2
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The 2t denominator should be enclosed in parentheses, but your work is otherwise correct.
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