Let's plot those three points:



Now let's draw the chord from (-13,3) to (-1,3).  I'll draw it in green:



Now the perpendicular bisector of a chord must go through the center
of a circle.  Since the green chord is 12 units long and is horizontal,
its midpoint is 6 units left of (-1,3) and 6 units right of (-13,3).
So the midpoint of that chord is (-7,3).  So we draw the perpendicular
bisector of the green line.  I'll draw it in red:








Now since the third point
has the same x-coordinate -7, that means that the perpendicular bisector
of the green chord goes through that third point (-7,9).  Notice that
(-7,9) is exactly 6 units above (-7,3), and that the other two given
points are also exactly 6 units from (-7,3), so that means that the
circle's center IS the point (-7,3) and the green chord is a diameter of
the circle.  So (-7,3) is the center and the radius is 6.  And we can draw 
in the circle with center (-7,3) and radius 6:


 
Answer: center (-7,3).

Edwin