Answer: The equation of the circle with center (-7, -4) containing the point (-1, -8) is (x + 7)^2 + (y + 4)^2 = 52.
Step-by-step explanation: The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, we are given the center (-7, -4) and a point on the circle (-1, -8). We can use the distance formula to find the radius:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((-1 - (-7))^2 + (-8 - (-4))^2)
= sqrt(36 + 16)
= sqrt(52)
= 2sqrt(13)
Now we can substitute the values into the equation of a circle:
(x - (-7))^2 + (y - (-4))^2 = (2sqrt(13))^2
Simplifying:
(x + 7)^2 + (y + 4)^2 = 52
Therefore, the equation of the circle with center (-7, -4) containing the point (-1, -8) is (x + 7)^2 + (y + 4)^2 = 52.