the equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]the center is (h,k) and r=radius
the center is:
[tex]\begin{gathered} x_{center}=\frac{7+7}{2}=7 \\ y_{center}=\frac{3+5}{2}=4 \end{gathered}[/tex]h=7 k=4
and we can find the diameter as
[tex]\begin{gathered} d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \\ d=\sqrt[]{(7-7)^2+(5-3)^2} \\ d=\sqrt[]{2^2}=2 \end{gathered}[/tex]and r=d/2
so r=1
so the equation of the circle is:
[tex](x-7)^2+(y-4)^2=1^2[/tex]