Coordinate Geometry of the Circle: a circle with centre $(a,b)$ and radius $r$ has equation
Circle equation
$(x-a)^2 + (y-b)^2 = r^2$
So $(x-2)^2+(y-3)^2=25$ has centre $(2,3)$ and radius $5$ (since $\sqrt{25}=5$).
Remember
- Centre $=(a,b)$, radius $=\sqrt{r^2}$.
- $x^2+y^2=r^2$ is centred on the origin.