The equation of a circle is given in standard form. Complete parts a through c to follow the step by step process to sketch the graph of the circle.

left parenthesis x minus 2 right parenthesis squared plus left parenthesis y plus 7 right parenthesis squared equals 9(x−2)2+(y+7)2=9

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Part 1

​a)**** Determine the center and radius of the circle.

The center of the circle is 

enter your response here.

To determine the center and radius of the circle, we can use the standard form of a circle's equation:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius of the circle.

Given the equation of the circle:

\[
(x - 2)^2 + (y + 7)^2 = 9
\]

### Step 1: Identify the center \((h, k)\)
- The term \((x - 2)^2\) indicates that \(h = 2\).
- The term \((y + 7)^2\) can be rewritten as \((y - (-7))^2\), so \(k = -7\).

Thus, the center of the circle is:
\[
\text{Center} = (2, -7)
\]

### Step 2: Determine the radius \(r\)
The right-hand side of the equation is 9, which corresponds to \(r^2 = 9\). To find \(r\), take the square root of 9:

\[
r = \sqrt{9} = 3
\]

Thus, the radius of the circle is:
\[
\text{Radius} = 3
\]

Would you like further details or have any questions?

Here are some related questions to further explore this topic:
1. How do you plot the center and radius of a circle on a graph?
2. What is the general form of a circle’s equation, and how is it related to the standard form?
3. Can the center and radius of a circle be determined from the general form of the equation?
4. How does the equation change if the circle is translated horizontally or vertically?
5. What happens to the equation of the circle if the radius is doubled?

**Tip:** Always check whether the equation is in standard form before identifying the center and radius.

The equation of a circle is given in standard form. Complete parts a through c to follow the step-by-step process to sketch the graph of the circle. (x−2)^2 + (y+7)^2 = 9. Part 1: a) Determine the center and radius of the circle.

Learn how to find the center and radius of a circle from the equation (x−2)^2 + (y+7)^2 = 9. This tutorial explains key geometry concepts and steps for solving problems related to circles. Ideal for students in Grades 9-10.

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