"Circle x + y + DX + ey + F = 0 (d ^ 2 + e ^ 2-4f > 0) is symmetric with respect to the line y = X-1" means that the center of the circle is symmetric with respect to the line?

"Circle x + y + DX + ey + F = 0 (d ^ 2 + e ^ 2-4f > 0) is symmetric with respect to the line y = X-1" means that the center of the circle is symmetric with respect to the line?

It means that the center of the circle is on the straight line