Write the standard form of the equation and the general form of the equation of the circle with the radius of 3 and the center (-3,0).

The equation of a circle is typically represented in two forms: **standard form** and **general form**.

### 1. **Standard Form of the Equation of a Circle**
The standard form is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where:
- \((h, k)\) is the center of the circle,
- \(r\) is the radius.

For this problem:
- The center is \((-3, 0)\),
- The radius is \(3\).

Substituting these values into the standard form:
\[
(x - (-3))^2 + (y - 0)^2 = 3^2
\]
Simplifying:
\[
(x + 3)^2 + y^2 = 9
\]
So, the **standard form** of the equation is:
\[
(x + 3)^2 + y^2 = 9
\]

### 2. **General Form of the Equation of a Circle**
The general form is obtained by expanding the standard form and arranging it into:
\[
Ax^2 + Ay^2 + Bx + Cy + D = 0
\]

Starting with the standard form \((x + 3)^2 + y^2 = 9\), expand it:
\[
(x^2 + 6x + 9) + y^2 = 9
\]
Now subtract 9 from both sides:
\[
x^2 + 6x + y^2 = 0
\]
So, the **general form** of the equation is:
\[
x^2 + y^2 + 6x = 0
\]

### Summary:
- **Standard Form**: \((x + 3)^2 + y^2 = 9\)
- **General Form**: \(x^2 + y^2 + 6x = 0\)

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How do you find the center and radius from a circle's equation in general form?
2. What is the equation of a circle with a radius of 5 and center at (2, -3)?
3. How would the equation change if the radius doubled?
4. How do you convert the general form of a circle to its standard form?
5. How can you graph a circle from its standard form equation?

**Tip**: When converting between the standard and general forms of a circle, always complete the square if needed!

Learn how to write the standard and general forms of the equation of a circle with a radius of 3 and a center at (-3, 0). This solution covers important concepts in geometry and is suitable for students in Grades 9-11.

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