The equation provided is $(x - 9)^2 + (y + 3)^2 = 9$. This is the standard form of the equation of a circle, which is given by:

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

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

Step 1: Identifying the center

By comparing $(x - 9)^2 + (y + 3)^2 = 9$ to the standard form, we can see:

• $h = 9$
• $k = -3$

Thus, the center of the circle is $(9, -3)$.

Step 2: Identifying the radius

In the equation, $r^2 = 9$, so $r = \sqrt{9} = 3$.

Final Answer:

• Center: $(9, -3)$
• Radius: $3$

Would you like any further details or explanations on this?

Here are 5 related questions to deepen your understanding:

1. How would the equation change if the radius were doubled?
2. What is the general equation for a circle centered at the origin?
3. How do you derive the equation of a circle given three points on its circumference?
4. What transformations would shift the center of the circle to the origin?
5. How would you find the equation of a circle given its diameter?

Tip: Always remember that the radius is the square root of the number on the right-hand side of the circle equation!