ANSWER
(x - 2)² + (y - 3)² = 9
EXPLANATION
The equation of a circle with center (h, k) and radius r is
[tex](x-h)^2+(y-k)^2=r^2[/tex]In this problem, the center of the circle is point (2, 3) and we don't know the radius, but we do know a point where the circle passes (5, 3). The distance between the center and this point is the radius of the circle:
Since the center and the point are at the same y-coordinate, the distance - and therefore the radius - is the difference between the x-coordinates of the two points:
[tex]r=5-2=3[/tex]The equation then is:
[tex]\begin{gathered} (x-2)^2+(y-3)^2=3^2 \\ (x-2)^2+(y-3)^2=9 \end{gathered}[/tex]
