The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (3, 2) → h = 3 and k = 2.
The length of a radius is equal a distance between a center and a point (9, 3).
The formula of a distance:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute:
[tex]r=\sqrt{(3-2)^2+(9-3)^2}=\sqrt{1^2+6^2}=\sqrt{1+36}=\sqrt{37}[/tex]
Substitute to the equation of a circle:
[tex](x-3)^2+(y-2)^2=(\sqrt{37})^2\\\\\boxed{(x-3)^2+(y-2)^2=37}[/tex]
