Find the equation of director circle of the circle $(x - 2)^{2} + (y + 1)^{2} = 2$

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Solution

Centre & radius of given circle are (2, -1) & $\sqrt{2}$ respectively
Centre and radius of the director circle will be (2, -1) & $\sqrt{2} \times \sqrt{2} = 2$ respectively
$∴$ equation of director circle is $(x - 2)^{2} + (y + 1)^{2} = 4$
$∴ x^{2} + y^{2} - 4 x + 2 y + 1 = 0$

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