Equidistant

First, we need to define the locus of points equidistant from two given points. This would be the perpendicular bisector of the segment formed by those two points.

Now we can find the information about this segment. First, the slope is $\frac{1-3}{6-2}$ which equals $\frac{-1}{2}$ . Next, the midpoint of the segment is $(\frac{2+6}{2}, \frac{3+1}{2})$ which is $(4, 2)$ .

Using this, we can find the equation of the perpendicular bisector. Its slope would be the negative reciprocal of the segment's slope, which is $2$ . To finalize the equation, we can plug in the midpoint's coordinates into $y = ax - b$ to find $b$ . $2 = 2(4) - b$ , so $b = 6$ . Hence, $a + b = 8$ .