Final answer:
The new circle has a center at (4, -17) and a radius of 15 units, after shifting the original circle down 6 units and tripling its radius.
Step-by-step explanation:
The student has given the equation of a circle: (x-4)^2 + (y+11)^2 = 25.
Initially, the center of the circle is at point (4, -11) with a radius of 5 units (since the square of the radius is 25).
When the circle is shifted down by 6 units, the y-coordinate of the center decreases by 6.
Therefore, the new center is (4, -17). Subsequently, tripling the radius means the new radius is 15 units, three times the original radius.
Therefore, the center and radius of the new circle are (4, -17) and 15 units, respectively.