https://file.aiquickdraw.com/mathbot/file/1728945537711lws8pj1w.jpg

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!

Identify the center and radius of the circle C that is given by the equation (x − 9)² + (y + 3)² = 9.

Learn how to find the center and radius of a circle given by the equation (x − 9)² + (y + 3)² = 9. This problem covers key concepts in circle geometry and provides a detailed step-by-step solution. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation