Answer:
(x + 1)^2 + (y + 6)^2 = 25.
Explanation:
- The standard 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, the center of the circle is (-1, -6) and the radius is 5. Substituting these values into the equation, we get:
(x - (-1))^2 + (y - (-6))^2 = 5^2
- Simplifying and rearranging terms, we get:
(x + 1)^2 + (y + 6)^2 = 25
- Therefore, the standard equation of the circle with center (-1, -6) and radius 5 is (x + 1)^2 + (y + 6)^2 = 25.