The equation for a circle is given by:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where:} \\ \text{center}=(h,k) \\ r=\text{radius}=\frac{d}{2} \end{gathered}[/tex]so:
[tex]\begin{gathered} d=8 \\ r=\frac{8}{2}=4 \\ C(h,k)=(1,-3) \\ (x-1)^2+(y+3)^2=16 \end{gathered}[/tex]The point which lies on the circle will be the one which satisfies the equation, hence:
[tex]\begin{gathered} (1,5) \\ (1-1)^2+(5+3)^2=16 \\ 64\ne16 \\ ------------------- \\ (5,-3) \\ (5-1)^2+(-3+3)^2=16 \\ 16=16 \end{gathered}[/tex]
