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Let (h, k) be the centre of a circle with radius a.
Thus, its equation will be ${\left(x-h\right)}^{2}+{\left(y-k\right)}^{2}={a}^{2}$.

(i) Here, h = −2, k = 3 and a = 4

∴ Required equation of the circle:
${\left(x+2\right)}^{2}+{\left(y-3\right)}^{2}={4}^{2}$
$⇒{\left(x+2\right)}^{2}+{\left(y-3\right)}^{2}=16$

(ii) Here, h = a, k = b and radius = $\sqrt{{a}^{2}+{b}^{2}}$

∴ Required equation of the circle:
${\left(x-a\right)}^{2}+{\left(y-b\right)}^{2}={a}^{2}+{b}^{2}$

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