Find the equation of the circle with centre (–a, –b) and radius

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

$(x-h)^{2}+(y-k)^{2}=r^{2}$

It is given that centre $(h, k)=(-a,-b)$ and radius $(r)=\sqrt{a^{2}-b^{2}}$.

Therefore, the equation of the circle is

$(x+a)^{2}+(y+b)^{2}=\left(\sqrt{a^{2}-b^{2}}\right)^{2}$

$x^{2}+2 a x+a^{2}+y^{2}+2 b y+b^{2}=a^{2}-b^{2}$

$x^{2}+y^{2}+2 a x+2 b y+2 b^{2}=0$