Final answer:
The equation of the circle with center (-9,-5) containing the point (-18,7) is (x + 9)^2 + (y + 5)^2 = 225.
Step-by-step explanation:
To determine the equation of a circle with center (-9,-5) containing the point (-18,7), we can use the standard form of the equation of a circle: (x - h)^2 + (y - k)^2 = r^2.
In this equation, (h,k) represents the center of the circle, and r represents the radius.
Substituting the given values, we have (x + 9)^2 + (y + 5)^2 = r^2. Now, we need to find the radius. The distance between the center (-9,-5) and (-18,7) can be found using the distance formula:
√[(x2 - x1)^2 + (y2 - y1)^2].
Plugging in the values, the distance is
√[(-18 - (-9))^2 + (7 - (-5))^2] = √[(9)^2 + (12)^2] = √(81 + 144) = √(225) = 15.
Thus, the equation of the circle is (x + 9)^2 + (y + 5)^2 = 225.