Answer
Center: $(1, 2)$
Radius = $2$ units
Equation: $(x-1)^2+(y-2)^2=4$
Work Step by Step
The standard form of the equation of a circle is:
$(x-h)^2+(y-k)^2=r^2$
where the center of the circle is $(h,k)$ and the radius is $r$.
Here, the center of the circle is $(1,2)$ so $h=1$ and $k=2$.
The radius can be calculated as the distance between the given point on the circle and the center.
The distance formula can be applied here:
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, where the points are $(x_1,y_1)$ and $(x_2,y_2)$
Here the distance is:
$r=d=\sqrt{(1-1)^2+(2-0)^2}=\sqrt{0+4}=2$
Therefore the standard form of the equation is:
$(x-1)^2+(y-2)^2=2^2$
$(x-1)^2+(y-2)^2=4$
