I am wondering if I can express in a formal way the fact that all tangent lines to a curve are parallel in the following way:
$$\alpha(s)+\lambda(s)\alpha'(s)=k$$ where $\alpha$ is the curve and $k$ is a constant.
It would be correct to express the family of lines like this? I know it is a simple doubt but I am getting confused with the notation in my book, so I need to be sure. Thanks.