The equation of circle is
(x–h)2+(y–k)2 = r2 ....(i)
Since the circle passes through point (4, 5) and co-ordinates of centre are (2, 2)
∴ radius of circle = √(4−2)2+(5−2)2 = √4+9 = √13
Now the required equation of circle is (x–2)2+(y–2)2 = (√13)2
⇒ x2 + 4 – 4x + y2 + 4 – 4y = 13 ⇒ x2 + y2 – 4x – 4y – 5 = 0.