The equation of a circle with centre (h,k) and radius r is given as

(x-h)² + (y-k)²=r²

It is given that centre (h,k) = (-a, -b) and radius (r) =

(x + a)² +(y + b)² =

⇒ x² + 2ax + a² + y² + 2by + b² = a² – b²

⇒ x² + y² +2ax + 2by + 2b² = 0