Question:
Find the centre and radius of the circle $(x+5)^{2}+(y-3)^{2}=36$
Solution:
The equation of the given circle is $(x+5)^{2}+(y-3)^{2}=36$.
$(x+5)^{2}+(y-3)^{2}=36$
$\Rightarrow\{x-(-5)\}^{2}+(y-3)^{2}=6^{2}$, 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.