> 
> $A(2 \cos \theta\_1 , 2 \sin \theta\_1)$ and $B(2 \cos \theta\_2 , 2 \sin \theta\_2)$ are two end points of a variable chord $AB$ of the circle, and $M$ is the midpoint of the chord. Suppose that the slope of the chord $AB$ is $\textbf{always}$ equal to $m$. Find the equation of the locus of $M$.
> 
> 
> 

While trying to solve the problem I found that:

* Equation of the circle is $x^2 + y^2 = 4$
* Coordinates of chord midpoint $M$ are $\left( \cos \theta\_1 + \cos \theta\_2 , \sin \theta\_1 + \sin \theta\_2 \right)$
* Slope of chord AB is $m = 
\dfrac{\sin \theta\_2 - \sin \theta\_1}{ \cos \theta\_2 - \cos \theta\_1}$

What should I do to get the solution: $x + my = 0$ ?