the centre of the given circle is (5.-7)

[draw a rough figure n observe.draw the tangents n chord of contact wrt (1,1)]

now,the line joining the centre of given circle and point of contact of either of the two tangents is the radius of the given circle .....and is obviously perpendicular to the tangents.

=> this angle is an angle in semicircle ....so the required circumcircle has (1,1) and  (5.-7)

as the extremities of diameter.

so its centre is (3,-3) and radius is