Final answer:
The center of the circle that lies in the second quadrant and is tangent to the lines x = -14, x = 8, and y = -4 is at the point (-3, -15).
Step-by-step explanation:
The question pertains to finding the center of a circle that lies in the second quadrant and is tangent to the vertical lines x = -14 and x = 8, as well as the horizontal line y = -4.
To find the center, consider the circle tangent to x = -14 and x = 8. The distance between these lines is the diameter of the circle, so the x-coordinate of the center is the average of -14 and 8, which is -3. For the y-coordinate, since the circle is tangent to y = -4 and the center lies in the second quadrant, the y-coordinate will be less than -4. Considering that the radius is half the diameter, we can find the radius by subtracting -14 from 8, dividing by 2, and taking the absolute value, which gives us 11. Hence, the y-coordinate of the center is -4 - 11 = -15.
The center of the circle is at the point (-3, -15).