Equation of the circle with center $(-a, -b)$ and radius $\sqrt{a^2 - b^2}$ is:
$x^2 + y^2 - 2ax - 2by - 2b^2 = 0$
$x^2 + y^2 - 2ax + 2by + 2a^2 = 0$
$x^2 + y^2 + 2ax + 2by + 2b^2 = 0$
$x^2 + y^2 - 2ax - 2by + 2b^2 = 0$
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