If the center of x ^ 2 + y ^ 2 + DX + ey + F = 0 (d ^ 2 + e ^ 2-4f > 0) is on the straight line x + y = 0, then the relation of D, e, f What does F have to do with them

If the center of x ^ 2 + y ^ 2 + DX + ey + F = 0 (d ^ 2 + e ^ 2-4f > 0) is on the straight line x + y = 0, then the relation of D, e, f What does F have to do with them

x^2+y^2+dx+ey+f=(x+d/2)^2 + (y+e/2)^2 + f -d^2/4 - e^2/4=0,
So if the center of the circle is (- D / 2, - E / 2), then - D / 2 - E / 2 = 0
So D + e = 0
The relation with F is d ^ 2 + e ^ 2-4f > 0