The standard form of the equation of a circle is:

$(x - h)^2 + (y - k)^2 = r^2$

Where:

• $(h, k)$ is the center of the circle.
• $r$ is the radius.

Given the equation:

$(x + 5)^2 + (y + 6)^2 = 81$

This can be rewritten as:

$(x - (-5))^2 + (y - (-6))^2 = 81$

By comparing this with the standard form, we can determine:

• The center is $(-5, -6)$.
• The radius is $\sqrt{81} = 9$.

Final Answer:

• The center of the circle is $(-5, -6)$.
• The radius is $9$.

Would you like further explanation or have any other questions? Here are some related questions to consider:

1. What is the general method for finding the center of a circle from its equation?
2. How do you sketch the graph of a circle given its center and radius?
3. Can you derive the equation of a circle from given points on the circumference?
4. What changes in the equation if the circle is shifted to a new location?
5. How do you find the equation of a circle given its diameter?

Tip: Always ensure the equation is in standard form before identifying the center and radius.