August 10th, 2017, 05:18 AM  #1 
Member Joined: May 2017 From: Slovenia Posts: 52 Thanks: 0  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^2z^2=1 x+y+z=0 Trying to parametrize this, I got: z=xy x^2+y^2(xy)^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 06:22 AM. 
August 10th, 2017, 06:31 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,725 Thanks: 1359 
The 2t denominator should be enclosed in parentheses, but your work is otherwise correct.


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