Question:
Find the equation of the circle with centre $(1,1)$ and radius $\sqrt{2}$
Solution:
The equation of a circle with centre (h, k) and radius r is given as
$(x-h)^{2}+(y-k)^{2}=r^{2}$
It is given that centre $(h, k)=(1,1)$ and radius $(r)=\sqrt{2}$.
Therefore, the equation of the circle is
$(x-1)^{2}+(y-1)^{2}=(\sqrt{2})^{2}$
$x^{2}-2 x+1+v^{2}-2 y+1=2$
$x^{2}+y^{2}-2 x-2 y=0$