Tangent vector to a curve

Say I have a curve in parametric form defined as:
b: t->(x(t),y(t)) for t1<t<t2
And then I work out the tangent vector as something like v=(-1,0).
So I'm trying to work out where the tangent is horizontal and vertical.

But I'm thinking that because the tangent vector has no t dependence, there aren't any tangents??

Is this right?

Do you have an actual example? It's hard to comment based on just what you've put there!

t->(t^2,t) -1<t<1
So for this one I got the tangent vector to be (2t,1) so I said there is a vertical tangent at (0,1), but then I don't think there can be a horizontal one, but I'm just trying to work out how to explain properly why there isn't based on the tangent vector I worked out.

Sorry for not being clear in the first post!

OK.

I'm out of practice on "tangent vectors" as part of a uni course. The "A level" explanation would be something like: if x = t^2 and y = t then dy/dx = (dy/dt)/(dx/dt) = 1/(2t). This can never equal 0 for finite t so there is no horizontal tangent to the curve. As t->0 then dy/dx becomes undefined so there is a vertical tangent.

Would this be acceptable for your course or can you adapt my wording in terms of tangent vectors?