Question:
This circle passes through the points $(-1, 2)$, $(3,0)$ and $(9,0)$. The center of the circle is at $(h,k)$. What is the value of $h+k$?

Answer:
The center of the circle must lie on the perpendicular bisector of the points $(3,0)$ and $(9,0),$ which is the line $x = 6,$ so $h = 6.$  Thus, the center of the circle is $(6,k).$

This point must be equidistant to $(-1,2)$ and $(3,0),$ so
\[7^2 + (k - 2)^2 = 9 + k^2.\]This gives us $k = 11.$  Hence, $h + k = 6 + 11 = \boxed{17}.$