Answer
$\color{blue}{(x-5)^2+(y-6)^2=10}$
Work Step by Step
RECALL:
The center-radius form of a circle whose center is at $(h, k)$ and whose radius is $r$ units is:
$(x-h)^2+(y-k)^2=r^2$
The given circle has its center at $(5, 6)$
Thus, the tentative equation of the circle is :
$(x-5)^2+(y-6)^2=r^2$
To find the value of $r^2$, substitute the x and y values of the point $(4, 9)$ to obtain:
$(4-5)^2+(9-6)^2=r^2
\\(-1)^2+3^2=r^2
\\1+9=r^2
\\10=r^2$
Therefore, the equation of the circle is:
$\\\color{blue}{(x-5)^2+(y-6)^2=10}$