Substititute the points in the equation to check which point lie on the circle.
[tex]\begin{gathered} (13-3)^2+(-1+1)^2=20 \\ (10)^2=20 \\ 100\ne20 \end{gathered}[/tex]Point (7,-3),
[tex]\begin{gathered} (7-3)^2+(-3+1)^2=20 \\ 16+4=20 \\ 20=20 \end{gathered}[/tex]Point (7,-3) lies on the circle.
For point (5,-3),
[tex]\begin{gathered} (5-3)^2+(-3+1)^2=20 \\ 4+4=20 \\ 8\ne20 \end{gathered}[/tex]For point (-1,1),
[tex]\begin{gathered} (-1-3)^2+(1+1)^2=20 \\ (-4)^2+(2)^2=20 \\ 16+4=20 \\ 20=20 \end{gathered}[/tex]Point (-1,1) lie on the circle.
For point (1,-3),
[tex]\begin{gathered} (1-3)^2+(-3+1)^2=20 \\ 4+4=20 \\ 8\ne20 \end{gathered}[/tex]So points lie on the circle are (7,-3) and (-1,1).
