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(A) The equation of a circle with centre $(h, k)$ and radius $r$ is given by $(x-h)^{2}+(y-k)^{2}=r^{2}$.Given centre $(h, k) = (-a, -b)$ and radius $

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$x^{2}+y^{2}+2ax+2by+2b^{2}=0$

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(A) The equation of a circle with centre $(h, k)$ and radius $r$ is given by $(x-h)^{2}+(y-k)^{2}=r^{2}$.Given centre $(h, k) = (-a, -b)$ and radius $r = \sqrt{a^{2}-b^{2}}$.Substituting these values into the standard equation:$(x - (-a))^{2} + (y - (-b))^{2} = (\sqrt{a^{2}-b^{2}})^{2}$$(x+a)^{2} + (y+b)^{2} = a^{2}-b^{2}$Expanding the squares:$x^{2} + 2ax + a^{2} + y^{2} + 2by + b^{2} = a^{2} - b^{2}$Subtracting $a^{2}$ from both sides and adding $b^{2}$ to both sides:$x^{2} + y^{2} + 2ax + 2by + b^{2} + b^{2} = 0$$x^{2} + y^{2} + 2ax + 2by + 2b^{2} = 0$

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

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