### Instruction: A hyperbola has its two foci at $(5, 0)$ and $(9, 4).$ Find the coordinates of its center.### Response: So the hyperbola's center is the midpoint of the line segment connecting the two foci.
Right, so we just need to find the midpoint of the line segment connecting $(5,0)$ and $(9,4)$.
The $x$-coordinate of the midpoint is the average of the $x$-coordinates of the endpoints, so it is $\frac{5+9}{2}=7$.
The $y$-coordinate of the midpoint is the average of the $y$-coordinates of the endpoints, so it is $\frac{0+4}{2}=2$.