Distance between points - equation of a line I have worked on this particular example: 
The distance between the point $M_1(3,2)$ and $A$ is $2\sqrt5$ and the distance between the point $M_2(-2, 2)$ and $B$ is $\sqrt5$. Come up with a equation for the line going through $A$ and $B$. 
I have tried playing around with the equations for the circles with centers in $M_1$ and $M_2$ respectively (the radii being the distance between $M_1$ and $A$, that is the distance between $M_2$ and $B$ for the other circle), but I am stuck. 
Would appreciate any help.
Thanks in advance. 
P.S. I am probably wrong but, isn't there infinitely many solutions since with the data I'm given I am basically being asked to come up with a particular equation for a line connecting any two points on those circles ? 

Hint:
As noted in the other answer your intuition that there are infinitely many solutions is correct.
 All these soution  can be represented as a family of straight lines dependent on a parameter in this way:
1) Represent the points $P_1$ of the circle of center $O_1=(\alpha_1,\beta_1)$ and radius $r_1$ in parametric form as:
$$
P_1=(\alpha_1 + r_1 \cos \theta, \beta_1+r_1 \sin \theta)
$$
an do the same for the other circle  of center $O_2=(\alpha_2,\beta_2)$ and radius $r_2$ 
$$
P_2=(\alpha_2 + r_2 \cos \theta, \beta_2+r_2 \sin \theta)
$$
now the equations of the straight lines passing thorough $P_1$ and $P_2$ have the form:
$$
y-(\alpha_1 +r_1\sin \theta)=\dfrac{\beta_1-\beta_2+(r_1-r_2)\sin \theta}{\alpha_1-\alpha_2+(r_1-r_2)\cos \theta} \left(x-(\alpha_1+r_1\cos \theta)  \right)
$$
