What is the general equation of lines going through 'a' particular point? I want to know the general equation of lines going through a single point where there will be arbitary constants which will change and cause the line to rotate in a circle and consequently the center will be the given point

Its known as family of lines its $$(ax+by+c)+\lambda(dx+ey+f)=0$$ where $\lambda$=arbitrary constant.
EDIT 
if we know the angle we can use rotation matrix to get new equation which is 
$$\left(\begin{matrix} \cos\theta& \sin\theta\\-\sin\theta & \cos\theta\end{matrix}\right)$$
