Answer
$(x-1)^{2}+(y-2)^{2}=2$
Work Step by Step
The standard form of an equation of a circle with radius $r$ and center $(h,k)$ is
$(x-h)^{2}+(y-k)^{2}=r^{2}$
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The center of the circle is the midpoint of the two given points on its diameter.
$C=(h,k)=\displaystyle \left(\frac{0+2}{2},\frac{1+3}{2}\right)=(1,2)$
The radius is the distance from $(1,2)$ to $(2,3)$.
$r=\sqrt{(2-1)^{2}+(3-2)^{2}}=\sqrt{2}$
Circle equation:
$(x-1)^{2}+(y-2)^{2}=2$
