Answer:
(x + 1)^2 + (y + 5)^2 = 169
Explanation:
The equation of a circle centered at (h,k) with radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
To find the equation of the circle, we first need to find the center and the radius.
Given that the circle is centered at (-1,-5), h = -1 and k = -5.
Next, we need to find the radius. To do this, we use the point (0,-18) that lies on the circle and use the distance formula:
r = sqrt[ (0-(-1))^2 + (-18-(-5))^2 ] = sqrt[ 1^2 + (13)^2 ] = sqrt[1 + 169] = sqrt[170] = 13
So, the equation of the circle is:
(x + 1)^2 + (y + 5)^2 = 13^2
Therefore, the equation of the circle centered at (-1,-5) that passes through (0,-18) is:
(x + 1)^2 + (y + 5)^2 = 169