Find the centre and radius of the circle $(x + 5)^{2} + (y - 3)^{2} = 36$

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Solution

The equation of the given circle is,
$(x + 5)^{2} + (y - 3)^{2} = 36$
$\Rightarrow {x - (- 5)}^{2} + {(y - 3)}^{2} = 6^{2}$
which is of the form $(x - h)^{2} + (y - k)^{2} = r^{2}$
where $h = - 5, k = 3$ and $r = 6$
Thus the centre of the given circle is $(- 5, 3)$ while its radius is $6$

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