Since the question asks for the slope, we can translate the coordinates without effecting the result, set (17,76) to be the new origin, then the centers of the 3 circles are (-3,16),(0,0) and (2,8), plot the circles out and you will notice that there is no way to draw a line through the origin and go between the other two circles, therefore the line must cut through the other 2 circles, and in order to satisfy the area condition, the line must be unique.