Question:
Find the centre and radius of each of the following circles :
$(x-3)^{2}+(y-1)^{2}=9$
Solution:
The general form of the equation of a circle is:
$(x-h)^{2}+(y-k)^{2}=r^{2}$
Where, (h, k) is the centre of the circle.
r is the radius of the circle.
Comparing the given equation of circle with general form we get:
$h=3, k=1, r^{2}=9$
$\Rightarrow$ centre $=(3,1)$ and radius $=3$ units.
Ans: centre = (3, 1) and radius = 3 units.