Final answer:
The values of a are 10 and -10, and the values of b are 2√11 and -2√11.
Step-by-step explanation:
To find the values of a and b, we can substitute the given coordinates into the equation of the circle. Let's start with the point (a,5):
(a)² + 5² = 125
a² + 25 = 125
a² = 100
a = ±10
So, the values of a are 10 and -10.
Now, let's substitute the other given point (9,b) into the equation:
9² + b² = 125
81 + b² = 125
b² = 44
b = ±√44
b = ±2√11
Therefore, the values of b are 2√11 and -2√11.