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The problem in the image asks to write the standard and general forms of the equation of a circle given its center and radius, then graph the circle. Let's break down the solution step-by-step:

### Given Information:
- Center of the circle: \( (h, k) = (-3, 0) \)
- Radius: \( r = 3 \)

### 1. Standard Form of the Circle Equation:
The standard form of the equation of a circle is:

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

Substituting the given values:

\[
(x - (-3))^2 + (y - 0)^2 = 3^2
\]

Simplify this:

\[
(x + 3)^2 + y^2 = 9
\]

### 2. General Form of the Circle Equation:
Expand the standard form to get the general form:

\[
(x + 3)^2 + y^2 = 9
\]

Expanding \( (x + 3)^2 \):

\[
x^2 + 6x + 9 + y^2 = 9
\]

Simplify this equation by subtracting 9 from both sides:

\[
x^2 + y^2 + 6x = 0
\]

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

Would you like further details, or do you have any questions?

### Related Questions:
1. How do you find the radius and center of a circle from its equation?
2. What are the steps to convert a circle's general form to the standard form?
3. How do you graph a circle given its equation?
4. What is the difference between the standard and general forms of a circle's equation?
5. How can completing the square be used to rewrite the general form of a circle?

**Tip**: Always check if you can simplify the general form by combining like terms or removing constants to match standard equations.

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

Learn how to write the standard and general form of a circle's equation, given its radius and center. This problem explains how to derive both forms step-by-step, including how to graph the circle. Suitable for high school students studying algebra and geometry.

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