Final answer:
The equation of the circle with center (5, -6) containing the point (11, -3) is (x - 5)² + (y + 6)² = 45.
Step-by-step explanation:
To determine the equation of a circle with center (5, -6) containing the point (11, -3), we can use the general equation of a circle: (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Given that the center is (5, -6), we can substitute these values into the equation to get: (x - 5)² + (y - (-6))² = r².
Now, let's find the radius. Since the circle contains the point (11, -3), we can substitute these values into the equation to get: (11 - 5)² + (-3 - (-6))² = r². Simplifying, we have: 6² + 3² = r². This gives us 45 = r². So the equation of the circle is: (x - 5)² + (y + 6)² = 45.