Question:
Find the centre and radius of each of the following circles :
$x^{2}+(y-1)^{2}=2$
Solution:
The general form of the equation of a circle is:
$(x-h)^{2}+(y-k)^{2}=r^{2}$
Where, $(\mathrm{h}, \mathrm{k})$ is the centre of the circle.
$r$ is the radius of the circle.
Comparing the given equation of circle with general form we get:
$h=0, k=1, r^{2}=2$
$\Rightarrow$ centre $=(0,1)$ and radius $=\sqrt{2}$ units.
Ans: centre $=(0,1)$ and radius $=\sqrt{2}$ units .