Explanation:
The coordinate of the center is given below as
[tex]\begin{gathered} A=(3,2) \\ A(h,k)=(3,2) \end{gathered}[/tex]
From the image below
The general equation of a circle is represented below as
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (h,k)=center \\ r=radius \end{gathered}[/tex]
To figure out the value for r, we will use the formula below
[tex]\begin{gathered} r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ x_1=3,x_2=7 \\ y_1=2,y_2=2 \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ r=\sqrt{(7-3)^2+(2-2)^2} \\ r=\sqrt{4^2+0^2} \\ r=\sqrt{16} \\ r=4 \\ r^2=16 \end{gathered}[/tex]
Hence,
The final answer by substituting the center and the radius will be given below as
[tex]\begin{gathered} (x-h)^{2}+(y-k)^{2}=r^{2} \\ (x-3)^2+(y-2)^2=16 \end{gathered}[/tex]
Hence,
The final answer is
[tex](x-3)^{2}+(y-2)^{2}=16[/tex]
