Question regarding tangents? Q : Find the equation of the  line that passes through the origin of the coordinations  and the focus of the parabola $y=x^2+4x+1$.. so I found the focus $( -2;-3)$ and the line that passes through the origin is $y=x$..now what?

I dunno how you found $y=x$ but if the focus is indeed $(-2,-3)$ then the equation of the line joining the origin and the focus is $$\cfrac {y-0}{x-0}= \cfrac{-3-0}{-2-0}$$
EDIT:
Having checked, the focus you found is incorrect, the focus of a parabola $ax^2+bx+c=0$ is the point $$\left(-\cfrac{b}{2a}, \cfrac{1-b^2+4ac}{4a}\right)= \left(-2,-\cfrac{11}{4} \right)$$
And the equation of the line joining the focus$\left(-2,-\cfrac{11}{4} \right)$ and the origin $O(0,0)$ is $$\cfrac {y-0}{x-0}= \cfrac{(-11/4)-0}{-2-0} \implies y=\cfrac{11}{8}x$$
My guess is that you mistook the focus for the vertex $=\left(-\cfrac{b}{2a}, \cfrac{-b^2+4ac}{4a}\right)$
