ANSWER
[tex](x+5)^2+(y-1)^2=9[/tex]
EXPLANATION
We want to find the equation that represents the circle given.
The general form for the equation of a circle is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where (a, b) = center of the circle
r = radius of the circle.
From the graph, the center of the circle, K, is given as (-5, 1)
To find the radius of the circle, we have to find the distance from the center of the circle to any point on its circumference.
Let us use (-2, 1)
The formula for distance between two points is given as:
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, the radius is:
[tex]\begin{gathered} r=\sqrt[]{(-2-(-5))^2+(1-1)^2}=\sqrt[]{(-2+5)^2+(1-1)^2} \\ r=\sqrt[]{3^2+0^2}=\sqrt[]{3^2} \end{gathered}[/tex]
From there, we can find the square of both sides of the equation to find r²:
[tex]\begin{gathered} r^2=3^2 \\ r^2=9 \end{gathered}[/tex]
Therefore, the equation of the circle in the given graph is:
[tex]\begin{gathered} (x-(-5))^2+(y-1)^2=9 \\ (x+5)^2+(y-1)^2=9 \end{gathered}[/tex]
