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 ? 

The way the question stands now, it has no answer. You do not know exactly where $A$ and $B$ are, as you only know they both lie on a circle. However, without knowing any other information, there are infinitely many pairs of points $A,B$ that satisfy your condition, and each will yield a different line.
