Defining tangent line using new parameter to a curve

Hi,

I have been asked a series of questions on the following curve

r(t) = (1+cost,2sint,0) where t varies from 0 to 2pi

part a) required me to find the orientation of the tangent vector point (pi/3)

I found the tangent vector r'(t)= (-sint,2cost,0) and substituted in (pi/3)

r'(pi/3)= -sqrt(3)/2 **i** +** j**

but part b) requires me to use a second parametric variable to define the tangent line to the point (pi/3).

I knwo this isnt to hard , but i dont quite understand what the question is asking. What do they mean define? have i not already defined it at this point? btw the answer given is q(s)=(1.5-sqrt(3)s/2, sqrt(3) + s ,0)

Any help understanding this would be appreciated