Mathematics

The key here is recognizing that a circle's equation is completely determined by its center and any point on it. Since you know the center $(2, 2)$ and a point $(4, 5)$ that lies on the circle, you can find the radius using the distance formula—that's the distance from center to the point. Once you have the radius $r$, the standard form $(x - h)^2 + (y - k)^2 = r^2$ gives you the equation immediately.

The key here is recognizing that a circle's equation is completely determined by its center and any point on it. Since you know the center $(2, 2)$ and a point $(4, 5)$ that lies on the circle, you can find the radius using the distance formula—that's the distance from center to the point. Once you have the radius $r$, the standard form $(x - h)^2 + (y - k)^2 = r^2$ gives you the equation immediately.