Question

Find the equation of the circle with centre $(-a,-b)$ and radius $\sqrt{a^2-b^2}$

Answer 1

Here it is given that centre $(h,k)=(-a,-b)$ and radius $r=\sqrt{a^2-b^2}$
Therefore the equation of the circle is
${(x+a)}^2+{(y+b)}^2={\left(\sqrt{a^2-b^2}\right)}^2$
$\Rightarrow x^2+2ax+a^2+y^2+2by+b^2=a^2-b^2$
$\Rightarrow x^2+y^2+2ax+2by+2b^2=0$