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Question:
Find the centre and radius of each of the following circles :
$\left(x-\frac{1}{2}\right)^{2}+\left(y+\frac{1}{3}\right)^{2}=\frac{1}{16}$
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:
$\mathrm{h}=1 / 2, \mathrm{k}=-1 / 3, \mathrm{r}^{2}=1 / 16$
$\Rightarrow$ centre $=(1 / 2,-1 / 3)$ and radius $=1 / 4$ units.
Ans: centre $=(1 / 2,-1 / 3)$ and radius $=1 / 4$ units.
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