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September 10th, 2017, 09:31 AM   #1
Joined: May 2017
From: Slovenia

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Osculating circle

I need to find the osculating circle of curve p(t) =( 4cos(t)-1; 3t; -4sin(t)) at T(3,0,0).

So I have found:

t = 0

N(t) = (-cos(t), 0, sin(t))

k(t) = 4/25

r(t) =1/k = 25/4 this is the radius.

The center is: p(t) + r(t)N(t)
That is: (3,0,0) + 25/4(-1,0,0) = (-13/4, 0, 0)

So I have the radius and the center but I'm not sure what to do next.
Their answer is :

p(phi) = (-13/4-25/4cos(x), 15/4sin(x), -5sin(x))
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