The equation of a circle with center (a, b) and radius r is
[tex](x-a)^2+(y-b)^2=r^2[/tex]We are given the center as
[tex](a,b)\Rightarrow(-14,9)[/tex]To find the radius, we can use the formula to find the distance between two points, that is, the point on the circle and the center.
[tex]r=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2_{}_{}}[/tex]where (x₁, y₁) = (-14, 9)
(x₂, y₂) = (-11, 12)
Thus, we have
[tex]\begin{gathered} r=\sqrt[]{(12-9)^2+(-11-\lbrack-14\rbrack)^2} \\ r=\sqrt[]{3^2+3^2} \\ r=\sqrt[]{9+9} \\ r=\sqrt[]{18} \\ r=3\sqrt[]{2} \end{gathered}[/tex]Therefore, inputting all the values into the equation for a circle, we have
[tex]\begin{gathered} (x-\lbrack-14\rbrack)^2+(y-9)^2=3\sqrt[]{2} \\ \therefore \\ (x+14)^2+(y-9)^2_{^{}}=3\sqrt[]{2} \end{gathered}[/tex]