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

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Solution

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
${(x + a)}^{2} + {(y + b)}^{2} = {(\sqrt{a^{2} - b^{2}})}^{2}$
$\Rightarrow x^{2} + 2 a x + a^{2} + y^{2} + 2 b y + b^{2} = a^{2} - b^{2}$
$\Rightarrow x^{2} + y^{2} + 2 a x + 2 b y + 2 b^{2} = 0$

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