Find the centre and radius of each of the following circles :

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 .

 

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