If the circle x ^ 2 + y ^ 2 + DX + ey + F = 0 (d ^ 2 + e ^ 2-4f > 0) is symmetric with respect to the line y = x + 1, then A D+E=2 B D+E=1 C D-E=2 D D-E=1

If the circle x ^ 2 + y ^ 2 + DX + ey + F = 0 (d ^ 2 + e ^ 2-4f > 0) is symmetric with respect to the line y = x + 1, then A D+E=2 B D+E=1 C D-E=2 D D-E=1

C
On the symmetry of the line y = x + 1, that is, the center of the circle is on the line
Let the center of the circle be (a, a + 1) and the radius be B, then (x-a) ^ 2 + [y - (a + 1)] ^ 2 = B ^ 2,
Expand x ^ 2 + y ^ 2-2ax-2 (a + 1) y + A ^ 2 + (a + 1) ^ 2-B ^ 2 = 0
In the corresponding topic, x ^ 2 + y ^ 2 + DX + ey + F = 0
D=-2a,E=-2(a+1),
Then d + e = - 4a-2, D-E = 2
So the answer is C