Firstly, calculate the radius r of the circle using distance between two points
[tex]\begin{gathered} r\text{ = }\sqrt[]{(2-(-1))2+(9-5)^2} \\ r=\text{ }\sqrt[]{(2+1)^2+(4)^2} \\ r=\sqrt[]{3^2+4^2} \\ r=\sqrt[]{9+16} \\ r=\sqrt[]{25} \\ r=\text{ 5} \end{gathered}[/tex]Then use the radius r=5 and the center (-1 , 5) to find the equation of the circle
[tex]\begin{gathered} r^2=(x-h)^2+(y-k)^2 \\ 5^2=(x-(-1))^2+(y-5)^2 \\ 5^2=(x+1)^2+(y-5)^2 \end{gathered}[/tex]The center radius form is
[tex]5^2=(x+1)^2+(y-5)^2[/tex]The standard form is
[tex]\text{ 25}^{}=(x+1)^2+(y-5)^2[/tex]