Final answer:
The center of the circle that lies in the fourth quadrant and is tangent to the lines x = 7, y = -4, and x = 17 is (12, -4).
Step-by-step explanation:
To find the center that lies in the fourth quadrant and is tangent to the lines x = 7, y = -4, and x = 17, we need to find the point where these lines intersect. The point of intersection will be the center of the circle. Since the tangents are vertical lines, the x-coordinate of the center will be the average of 7 and 17, which is 12. The y-coordinate of the center will be the y-coordinate of the tangent line y = -4, which is -4. Therefore, the center of the circle is (12, -4).