Let the coordinate of point N be N( 1, t), and calculate the distance from point N to line y=-x-3 with the distance formula from point to line, and let it be R. Because the circle centered on point N is tangent to y=-x-3, the calculated distance is the radius of the circle, and both points A and B are on the circle, so the radius of the circle is equal to the length of the line segment NA or NB.

R=|t+4|/√2 (obviously t >-4, so the absolute value sign can be removed); Na = Nb = √ (4+T 2) Let R=NA and T = 4 2 √ 6 be solvable.

So N(4+2√6) or (4-2√6)